Here - Laboratoire Kastler Brossel
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Abstracts<br />
Organised by Laurent Hilico, LKB, Université d’Evry-Val-d’Essonne, France<br />
and Martina Knoop, PIIM, Université de Provence, France<br />
Secretary : Frédérique Augougnon, Université d’Evry-Val-d’Essonne, France
This workshop has been endorsed by<br />
We acknowledge financial support by
Sponsors
Scientific committee<br />
Michael Drewsen<br />
Pierre Dubé<br />
Olivier Dulieu<br />
Giovanna Morigi<br />
Roee Ozeri<br />
Stephan Schiller<br />
Utako Tanaka<br />
Aarhus University, Denmark<br />
NRC, Canada<br />
CNRS, Orsay, France<br />
UAB, Barcelona, Spain<br />
Weizmann Institute, Israel<br />
Düsseldorf University, Germany<br />
Osaka University, Japan<br />
Organisers<br />
Laurent Hilico<br />
<strong>Laboratoire</strong> <strong>Kastler</strong>-<strong>Brossel</strong>, Université d’Evry<br />
France<br />
Martina Knoop<br />
Physique des Interactions Ioniques et Moléculaires<br />
CNRS - Université de Provence, France
Camping Els Prat
INDEX BY NAME<br />
AUTHOR AUTHORS TITLE<br />
Number<br />
Session<br />
Page<br />
AKERMAN Nitzan N. Akerman, S. Kotler and R. Ozeri Quantum information with Strontium ions at the Weizmann 2-01 I 37<br />
Institute<br />
ALBERT Magnus M. Albert, J.P.Marler, P.F.Herskind, A. Dantan, Cavity QED and Cavity Mediated Cooling Using Ion Coulomb 2-02 I 38<br />
M.B.Langkilde-Lauesen and M.Drewsen<br />
Crystals<br />
BERMUDEZ Alejandro A. Bermudez The Dirac Equation in Trapped ions 2-03 I 39<br />
BRÜSER Delia D. Brüser, T. Collath, D. Eiteneuer, M. Johanning, P.<br />
Kaufmann, P. Kunert, H. Wunderlich and C. Wunderlich<br />
Microstructured ion traps with magnetic gradients greater<br />
than 100 T/m<br />
1-01 I 19<br />
DE CHIARA Gabriele G. De Chiara, S. Fishman, T. Calarco and G. Morigi One-dimensional Coulomb chains at low temperatures 1-02 I 20<br />
DUBE Pierre P. Dubé, A. A. Madej, and J. E. Bernard The 88Sr+ Optical Frequency Standard at the National 3-01 I 53<br />
Research Council<br />
EBLE Johannes W. Schnitzler, N. M. Linke, J. Eble, F. Schmidt-Kaler, and Experimental demonstration of a deterministic single ion 1-11 II 29<br />
K. Singer<br />
source with an expected implantation resolution of a few nm<br />
ERLEKAM Undine C. F. Correia, U. Erlekam, P. Maître and G. Ohanessian Structural characterization of the protonated, phosphorylated 4-01 I 65<br />
dipeptide [Gly-pTyrH]+ in the gas phase<br />
GLORIEUX Quentin Q. Glorieux, R. Dubessy, B. Dubost, S. Removille, T. Generation of relative-intensity squeezed light using four-wave 2-04 I 40<br />
Coudreau, S. Guibal, L. Guidoni, J.P. Likformann, and N. mixing in an rubidium atomic vapor<br />
Sangouard, P. Milman<br />
GONCALVES DE BARROS Helena H. G. Barros, F. Dubin, C. Russo, A. Stute, P. O. From a single-photon emitter to a single ion laser 2-05 I 41<br />
Schmidt, and R. Blatt<br />
HASEGAWA Shuichi S. Hasegawa Isotope selective trapping with linear Paul traps 4-06 II 70<br />
HAUKE Philipp P. Hauke, R. Schmied, T. Roscilde, V. Murg, D. Porras, Quantum phases for the frustrated nearest-neighbor XY model 2-06 I 42<br />
and J. I. Cirac<br />
on the anisotropic triangular lattice<br />
HEMMERLING Börge B. Hemmerling, L. An der Lan, P. O. Schmidt Towards Direct Frequency Comb Spectroscopy Using 3-02 I 54<br />
Quantum Logic<br />
HILICO Laurent JP. Karr, V. I. Korobov, J. Pedregosa, F. Bielsa, A. H2+ vibrational spectroscopy : theoretical results and 3-03 I 55<br />
Douillet and L. Hilico<br />
experimental developments<br />
HUBER Gerhard G. Huber, W. Schnitzler, R. Reichle, K. Singer and F. Ion transport in a segmented Paul trap 1-03 I 21<br />
Schmidt-Kaler<br />
JILEK Mojmir M. Jilek, M. Hejduk, P. Dohnal, I. Korolov, R. Plašil, Cryogenic Electron-Ion Trap 1-04 I 22<br />
J.Glosík, T. Kotrik<br />
KELLER Matthias P. Blythe, A. Mortensen, N. Seymour-Smith, M. Keller Trapped Ion Cavity-QED: Interfacing Ions and Photons 2-07 II 43<br />
and W. Lange<br />
KHROMOVA Anastasiya A. Khromova, A. Varon, B. Scharfenberger, Ch. Piltz, Ch. A linear Paul Trap for ion spin molecules 1-05 I 23<br />
Wunderlich<br />
KIRCHMAIR Gerhard G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. High fidelity quantum gates with trapped 43 Ca + ions 1-06 I 24<br />
F. Roos, and R. Blatt<br />
KOTLER Shlomi N. Akerman, S. Kotler and R. Ozeri Quantum information with Strontium ions at the Weizmann<br />
Institute<br />
2-01 I 37<br />
KUNERT Peter D. Brüser, T. Collath, D. Eiteneuer, M. Johanning, P.<br />
Kaufmann, P. Kunert, H. Wunderlich and C. Wunderlich<br />
Microstructured ion traps with magnetic gradients greater<br />
than 100 T/m<br />
1-01 I 19<br />
LORENZ Ulrich U. J. Lorenz, A. Svendsen, O. V. Boyarkin and T. R. A tandem mass spectrometer for photodissociation<br />
4-02 I 66<br />
Rizzo<br />
spectroscopy of cold biomolecular ions in the gas phase<br />
MANE JUNIOR Ernesto E. Mané, J. Billowes, K. Blaum, P. Campbell, B. Cheal, D. Collinear laser spectroscopy with cooled and trapped 4-03 I 67<br />
Forest, K. Flanagan, G. Neyens, R. Neugart, G. Tungate, radioisotopes at ISOLDE<br />
P. Vingerhoets, D. Yordanov and The ISOLDE<br />
Collaboration<br />
MARCIANTE Mathieu M. Marciante, A. Calisti, C. Champenois, M. Knoop, F. Study of ion dynamics in a radiofrequency trap by molecular 1-07 I 25<br />
Vedel<br />
dynamics simulations<br />
MATJESCHK Robert R. Matjeschk A planar Paul trap 1-08 I 26<br />
MC LOUGHLIN James J. J. McLoughlin, A. H. Nizamani, J. D. Siverns, R. C. Towards ion trap array architectures with 171Yb+ ions 2-12 II 49<br />
Sterling, M. Bevan-Stevenson, N. Davies, J. Grove-Smith,<br />
M. Hughes, B. Johnson, K. Lee, B. S. Pruess, R.<br />
Ramasawmy, D. N. Scrivener, T. Short, and W. K.<br />
Hensinger<br />
MEHLSTAEUBLER Tanja B. Stein, T.E. Mehlstäubler, I. Sherstov, M. Okhapkin, B.<br />
171<br />
Yb + single-ion optical frequency standard 3-05 I 57<br />
Lipphardt, Chr. Tamm, E. Peik<br />
MIHALCEA Bogdan M. B. Mihalcea, O. S. Stoican, Gina T. Visan, L. M. Dinca Multipolar trap geometries for particle trapping under standard 1-09 II 27<br />
and I. N. Mihailescu<br />
reference temperature and pressure conditions<br />
MORTENSEN Anders P. Blythe, A. Mortensen, N. Seymour-Smith, M. Keller Trapped Ion Cavity-QED: Interfacing Ions and Photons 2-07 II 43<br />
and W. Lange<br />
NIEDERMAYR Michaël M. Niedermayr Towards Cryogenic Surface Ion Traps 1-10 II 28<br />
ODOM Brian B. Odom Search for Time-Variation of the Electron-Proton Mass Ratio 3-10 II 62<br />
with MilliKelvin Trapped Molecular Ions<br />
OFFENBERG David D. Offenberg, C. Zhang, B. Roth, and S. Schiller Towards sympathetic cooling of charged proteins 4-04 II 68<br />
PEDREGOSA GUTIERREZ Jofre J. Pedregosa Gutierrez, F. Bielsa, J-P. Karr, A. Douillet<br />
and L. Hilico<br />
Two photon ro-vibrational spectroscopy of H 2 + : From<br />
Hyperbolic to Linear RF trap<br />
3-04 II 56
REMOVILLE Sébastien S. Removille, R. Dubessy, Q. Glorieux, T. Coudreau, S.<br />
Guibal, L. Guidoni, J.P. Likforman, and N. Sangouard<br />
Towards a Quantum memory in trapped ions 2-08 II 44<br />
SCHILLER Stephan S. Vasilyev, S. Schiller, A. Nevsky, A. Grisard, D. Faye, E. Broadly tunable sub-mW CW Narrowband mid-IR Laser<br />
Lallier, Z. Zhang, A. J. Boyland, J. K. Sahu, M. Ibsen, W. Source for Molecular Spectroscopy<br />
A. Clarkson<br />
SCHNEIDER Christian C. Schneider, R. Matjeschk, and T. Schaetz Towards two-dimensionnal quantum simulations with trapped<br />
ions<br />
SCHNITZLER Wolfgang W. Schnitzler, N. M. Linke, J. Eble, F. Schmidt-Kaler, and<br />
K. Singer<br />
Experimental demonstration of a deterministic single ion<br />
source with an expected implantation resolution of a few nm<br />
3-06 II 58<br />
2-09 II 45<br />
1-11 II 29<br />
SCHULZ Stephan St. Schulz, U. Poschinger, F. Ziesel, G. Huber, F. Schmidt Sideband cooling and coherent dynamics in a microchip multisegmented<br />
1-14 II 32<br />
Kaler<br />
ion trap<br />
SEGAL Daniel D. Crick, S. Donnellan, H. Ohadi, I. Bhatti, R.C. Controlling the Motion of Small Numbers of Ions in a Penning 1-15 II 33<br />
Thompson and D.M. Segal,<br />
Trap<br />
SHU Gang G. Shu, N.Kurz, M.Dietrich, A.Kleczewski, G.Howell, Trapped Barium Ions for Quantum Computation, Atomic Clock 2-10 II 46<br />
R.Bowler, J.Salacka, P.Green, B.B.Blinov<br />
and Precise Measurement<br />
STEIN Björn B. Stein, T.E. Mehlstäubler, I. Sherstov, M. Okhapkin, B.<br />
171<br />
Yb + single-ion optical frequency standard 3-05 I 57<br />
Lipphardt, Chr. Tamm, E. Peik<br />
STOICAN Ovidiu O. Stoican, B. Mihalcea, L. Dinca, G. Visan Acoustic excitation of the charged microparticles motion in a 1-12 II 30<br />
linear electrodynamic trap<br />
SVENDSEN Annette U. J. Lorenz, A. Svendsen, O. V. Boyarkin and T. R. A tandem mass spectrometer for photodissociation<br />
4-02 I 66<br />
Rizzo<br />
spectroscopy of cold biomolecular ions in the gas phase<br />
TANAKA Utako U. Tanaka, R. Naka, F. Iwata, T. Ujimaru, K. R. Brown, I. Design and Characterization of a Planar Trap 1-13 II 31<br />
L. Chuang and S. Urabe<br />
THOMPSON Richard R.C. Thompson, D.M. Segal, S. Bharadia, W.<br />
An Ion Trap for laser spectroscopy of cold highly-charged ions 4-07 II 71<br />
Nörtershäuser, D.F.A. Winters, M. Vogel, Z. Andjelkovic<br />
and the SPECTRAP collaboration<br />
VON ZANTHIER Joachim J. von Zanthier, Ch. Thiel, Th. Bastin, G. S. Agarwal Quantum imaging with trapped ions 2-11 II 47<br />
WAGNER Anke A. Wagner, K. Blaum, W. Quint, B. Schabinger, S. Sturm Design of a battery-based low noise voltage source 3-07 I 59<br />
WERTH Guenter S. Kreim, J. Alonso, K. Blaum, H.-J. Kluge, W. Quint, B. Test of QED and CPT via g-factors 3-08 II 60<br />
Schabinger, S. Stahl, S. Ulmer, J. Verdu, M. Vogel, J.<br />
Walz, G. Werth<br />
WILLITSCH Stephan S. Willitsch, M. T. Bell, A. D. Gingell, J. M. Oldham and T. Cold Chemistry with Cold Ions 4-05 II 69<br />
P. Softley<br />
ZUMSTEG Cédric C. Zumsteg, C. Champenois, G. Hagel, M. Houssin, D.<br />
Guyomarc’h, F. Vedel, M. Knoop<br />
A single Ca + ion for optical frequency metrology 3-09 II 61
INDEX BY NUMBER<br />
AUTHOR AUTHORS TITLE<br />
BRÜSER Delia D. Brüser, T. Collath, D. Eiteneuer, M. Johanning, P.<br />
Kaufmann, P. Kunert, H. Wunderlich and C. Wunderlich<br />
KUNERT Peter D. Brüser, T. Collath, D. Eiteneuer, M. Johanning, P.<br />
Kaufmann, P. Kunert, H. Wunderlich and C. Wunderlich<br />
Microstructured ion traps with magnetic gradients greater<br />
than 100 T/m<br />
Microstructured ion traps with magnetic gradients greater<br />
than 100 T/m<br />
Number<br />
Session<br />
Page<br />
1-01 I 19<br />
1-01 I 19<br />
DE CHIARA Gabriele G. De Chiara, S. Fishman, T. Calarco and G. Morigi One-dimensional Coulomb chains at low temperatures 1-02 I 20<br />
HUBER Gerhard G. Huber, W. Schnitzler, R. Reichle, K. Singer and F. Ion transport in a segmented Paul trap 1-03 I 21<br />
Schmidt-Kaler<br />
JILEK Mojmir M. Jilek, M. Hejduk, P. Dohnal, I. Korolov, R. Plašil, Cryogenic Electron-Ion Trap 1-04 I 22<br />
J.Glosík, T. Kotrik<br />
KHROMOVA Anastasiya A. Khromova, A. Varon, B. Scharfenberger, Ch. Piltz, Ch. A linear Paul Trap for ion spin molecules 1-05 I 23<br />
Wunderlich<br />
KIRCHMAIR Gerhard G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. High fidelity quantum gates with trapped 43 Ca + ions 1-06 I 24<br />
F. Roos, and R. Blatt<br />
MARCIANTE Mathieu M. Marciante, A. Calisti, C. Champenois, M. Knoop, F. Study of ion dynamics in a radiofrequency trap by molecular 1-07 I 25<br />
Vedel<br />
dynamics simulations<br />
MATJESCHK Robert R. Matjeschk A planar Paul trap 1-08 I 26<br />
MIHALCEA Bogdan M. B. Mihalcea, O. S. Stoican, Gina T. Visan, L. M. Dinca Multipolar trap geometries for particle trapping under standard 1-09 II 27<br />
and I. N. Mihailescu<br />
reference temperature and pressure conditions<br />
NIEDERMAYR Michaël M. Niedermayr Towards Cryogenic Surface Ion Traps 1-10 II 28<br />
EBLE Johannes W. Schnitzler, N. M. Linke, J. Eble, F. Schmidt-Kaler, and Experimental demonstration of a deterministic single ion 1-11 II 29<br />
K. Singer<br />
source with an expected implantation resolution of a few nm<br />
SCHNITZLER Wolfgang W. Schnitzler, N. M. Linke, J. Eble, F. Schmidt-Kaler, and Experimental demonstration of a deterministic single ion 1-11 II 29<br />
K. Singer<br />
source with an expected implantation resolution of a few nm<br />
STOICAN Ovidiu O. Stoican, B. Mihalcea, L. Dinca, G. Visan Acoustic excitation of the charged microparticles motion in a 1-12 II 30<br />
linear electrodynamic trap<br />
TANAKA Utako U. Tanaka, R. Naka, F. Iwata, T. Ujimaru, K. R. Brown, I. Design and Characterization of a Planar Trap 1-13 II 31<br />
L. Chuang and S. Urabe<br />
SCHULZ Stephan St. Schulz, U. Poschinger, F. Ziesel, G. Huber, F. Schmidt Sideband cooling and coherent dynamics in a microchip multisegmented<br />
1-14 II 32<br />
Kaler<br />
ion trap<br />
SEGAL Daniel D. Crick, S. Donnellan, H. Ohadi, I. Bhatti, R.C. Controlling the Motion of Small Numbers of Ions in a Penning 1-15 II 33<br />
Thompson and D.M. Segal,<br />
Trap<br />
AKERMAN Nitzan N. Akerman, S. Kotler and R. Ozeri Quantum information with Strontium ions at the Weizmann 2-01 I 37<br />
Institute<br />
KOTLER Shlomi N. Akerman, S. Kotler and R. Ozeri Quantum information with Strontium ions at the Weizmann 2-01 I 37<br />
Institute<br />
ALBERT Magnus M. Albert, J.P.Marler, P.F.Herskind, A. Dantan, Cavity QED and Cavity Mediated Cooling Using Ion Coulomb 2-02 I 38<br />
M.B.Langkilde-Lauesen and M.Drewsen<br />
Crystals<br />
BERMUDEZ Alejandro A. Bermudez The Dirac Equation in Trapped ions 2-03 I 39<br />
GLORIEUX Quentin Q. Glorieux, R. Dubessy, B. Dubost, S. Removille, T. Generation of relative-intensity squeezed light using four-wave 2-04 I 40<br />
Coudreau, S. Guibal, L. Guidoni, J.P. Likformann, and N. mixing in an rubidium atomic vapor<br />
Sangouard, P. Milman<br />
GONCALVES DE BARROS Helena H. G. Barros, F. Dubin, C. Russo, A. Stute, P. O. From a single-photon emitter to a single ion laser 2-05 I 41<br />
Schmidt, and R. Blatt<br />
HAUKE Philipp P. Hauke, R. Schmied, T. Roscilde, V. Murg, D. Porras, Quantum phases for the frustrated nearest-neighbor XY model 2-06 I 42<br />
and J. I. Cirac<br />
on the anisotropic triangular lattice<br />
KELLER Matthias P. Blythe, A. Mortensen, N. Seymour-Smith, M. Keller Trapped Ion Cavity-QED: Interfacing Ions and Photons 2-07 II 43<br />
and W. Lange<br />
MORTENSEN Anders P. Blythe, A. Mortensen, N. Seymour-Smith, M. Keller Trapped Ion Cavity-QED: Interfacing Ions and Photons 2-07 II 43<br />
and W. Lange<br />
REMOVILLE Sébastien S. Removille, R. Dubessy, Q. Glorieux, T. Coudreau, S.<br />
Guibal, L. Guidoni, J.P. Likforman, and N. Sangouard<br />
Towards a Quantum memory in trapped ions 2-08 II 44<br />
SCHNEIDER Christian C. Schneider, R. Matjeschk, and T. Schaetz Towards two-dimensionnal quantum simulations with trapped 2-09 II 45<br />
ions<br />
SHU Gang G. Shu, N.Kurz, M.Dietrich, A.Kleczewski, G.Howell, Trapped Barium Ions for Quantum Computation, Atomic Clock 2-10 II 46<br />
R.Bowler, J.Salacka, P.Green, B.B.Blinov<br />
and Precise Measurement<br />
VON ZANTHIER Joachim J. von Zanthier, Ch. Thiel, Th. Bastin, G. S. Agarwal Quantum imaging with trapped ions 2-11 II 47<br />
MC LOUGHLIN James J. J. McLoughlin, A. H. Nizamani, J. D. Siverns, R. C. Towards ion trap array architectures with 171Yb+ ions 2-12 II 49<br />
Sterling, M. Bevan-Stevenson, N. Davies, J. Grove-Smith,<br />
M. Hughes, B. Johnson, K. Lee, B. S. Pruess, R.<br />
Ramasawmy, D. N. Scrivener, T. Short, and W. K.<br />
Hensinger<br />
DUBE Pierre P. Dubé, A. A. Madej, and J. E. Bernard The 88Sr+ Optical Frequency Standard at the National 3-01 I 53<br />
Research Council<br />
HEMMERLING Börge B. Hemmerling, L. An der Lan, P. O. Schmidt Towards Direct Frequency Comb Spectroscopy Using<br />
Quantum Logic<br />
3-02 I 54
HILICO Laurent JP. Karr, V. I. Korobov, J. Pedregosa, F. Bielsa, A. H2+ vibrational spectroscopy : theoretical results and 3-03 I 55<br />
Douillet and L. Hilico<br />
experimental developments<br />
PEDREGOSA GUTIERREZ Jofre J. Pedregosa Gutierrez, F. Bielsa, J-P. Karr, A. Douillet Two photon ro-vibrational spectroscopy of H + 2 : From 3-04 II 56<br />
and L. Hilico<br />
Hyperbolic to Linear RF trap<br />
MEHLSTAEUBLER Tanja B. Stein, T.E. Mehlstäubler, I. Sherstov, M. Okhapkin, B.<br />
171<br />
Yb + single-ion optical frequency standard 3-05 I 57<br />
Lipphardt, Chr. Tamm, E. Peik<br />
STEIN Björn B. Stein, T.E. Mehlstäubler, I. Sherstov, M. Okhapkin, B.<br />
171<br />
Yb + single-ion optical frequency standard 3-05 I 57<br />
Lipphardt, Chr. Tamm, E. Peik<br />
SCHILLER Stephan S. Vasilyev, S. Schiller, A. Nevsky, A. Grisard, D. Faye, E. Broadly tunable sub-mW CW Narrowband mid-IR Laser 3-06 II 58<br />
Lallier, Z. Zhang, A. J. Boyland, J. K. Sahu, M. Ibsen, W. Source for Molecular Spectroscopy<br />
A. Clarkson<br />
WAGNER Anke A. Wagner, K. Blaum, W. Quint, B. Schabinger, S. Sturm Design of a battery-based low noise voltage source 3-07 I 59<br />
WERTH Guenter S. Kreim, J. Alonso, K. Blaum, H.-J. Kluge, W. Quint, B. Test of QED and CPT via g-factors 3-08 II 60<br />
Schabinger, S. Stahl, S. Ulmer, J. Verdu, M. Vogel, J.<br />
Walz, G. Werth<br />
ZUMSTEG Cédric C. Zumsteg, C. Champenois, G. Hagel, M. Houssin, D. A single Ca + ion for optical frequency metrology 3-09 II 61<br />
Guyomarc’h, F. Vedel, M. Knoop<br />
ODOM Brian B. Odom Search for Time-Variation of the Electron-Proton Mass Ratio 3-10 II 62<br />
with MilliKelvin Trapped Molecular Ions<br />
ERLEKAM Undine C. F. Correia, U. Erlekam, P. Maître and G. Ohanessian Structural characterization of the protonated, phosphorylated 4-01 I 65<br />
dipeptide [Gly-pTyrH]+ in the gas phase<br />
LORENZ Ulrich U. J. Lorenz, A. Svendsen, O. V. Boyarkin and T. R. A tandem mass spectrometer for photodissociation<br />
4-02 I 66<br />
Rizzo<br />
spectroscopy of cold biomolecular ions in the gas phase<br />
SVENDSEN Annette U. J. Lorenz, A. Svendsen, O. V. Boyarkin and T. R. A tandem mass spectrometer for photodissociation<br />
4-02 I 66<br />
Rizzo<br />
spectroscopy of cold biomolecular ions in the gas phase<br />
MANE JUNIOR Ernesto E. Mané, J. Billowes, K. Blaum, P. Campbell, B. Cheal, D. Collinear laser spectroscopy with cooled and trapped 4-03 I 67<br />
Forest, K. Flanagan, G. Neyens, R. Neugart, G. Tungate, radioisotopes at ISOLDE<br />
P. Vingerhoets, D. Yordanov and The ISOLDE<br />
Collaboration<br />
OFFENBERG David D. Offenberg, C. Zhang, B. Roth, and S. Schiller Towards sympathetic cooling of charged proteins 4-04 II 68<br />
WILLITSCH Stephan S. Willitsch, M. T. Bell, A. D. Gingell, J. M. Oldham and T. Cold Chemistry with Cold Ions 4-05 II 69<br />
P. Softley<br />
HASEGAWA Shuichi S. Hasegawa Isotope selective trapping with linear Paul traps 4-06 II 70<br />
THOMPSON Richard R.C. Thompson, D.M. Segal, S. Bharadia, W.<br />
Nörtershäuser, D.F.A. Winters, M. Vogel, Z. Andjelkovic<br />
and the SPECTRAP collaboration<br />
An Ion Trap for laser spectroscopy of cold highly-charged ions 4-07 II 71
NOVEL ION TRAP DESIGN
Microstructured ion traps with magnetic gradients greater than 100 T/m<br />
Delia Brüser 1 , Thomas Collath 1 , Daniel Eiteneuer 1 , Michael Johanning 1 , Peter Kaufmann 1 , Peter<br />
Kunert 1 , Harald Wunderlich 1 and Christof Wunderlich 1<br />
1<br />
Working Group Quantenoptik, University of Siegen, Walter Flex Str. 3, 57072 Siegen<br />
Strings of laser cooled ions stored in microstructured Paul traps (Microtraps) have promising<br />
potential for quantum optics. They provide a system which can be screened from decohering<br />
environment, accurately prepared in a large variety of states and manipulated with high accuracy.<br />
Furthermore, state detection can be achieved with almost unit efficiency.<br />
We will expose Ytterbium ions to a magnetic field gradient. This allows us to address the ions in<br />
the frequency space [1], [2]. Furthermore, long distance spin-spin coupling of the ions’ internal<br />
states is induced by the gradient, which is proportional in strength to the square of the magnetic<br />
gradient [1]. The spin-spin coupling is useful for building a quantum computer, for quantum<br />
simulations and for studying quantum phase transitions.<br />
Microstructured current flow has proven successful in the<br />
creation of magnetic fields [3]. In those cases, large gradients are<br />
found only very close to the substrate surface. For our trap, the<br />
challenge is to create large gradients over extended ion strings as<br />
far away as possible from the surface to avoid heating which<br />
scales steeply with the ion surface separation.<br />
Our microtrap consists of a three layer structure (based on a<br />
design by F. Schmidt-Kaler et al., University of Ulm, see figure on<br />
the right). The outer layers apply DC and AC electric fields for<br />
3D trapping whilst the middle layer is used to form an<br />
inhomogeneous magnetic field. This is realized by having the electric current flow around the<br />
inner edge of the middle layer which works as a section of a circular coil (see figure below). We<br />
form an Anti Helmholtz coil by two of these geometries with opposite current flow.<br />
We want to achieve as large coupling constants as<br />
possible. Therefore, we need large gradients. A large<br />
magnetic gradient results in both large frequency<br />
separation and coupling constants. We developed a<br />
middle layer design which was optimized with respect to<br />
gradient per dissipated heat. From simulations and first<br />
tests with prototypes we expect this design to allow gradients greater than 100 T/m.<br />
[1] F. Mintert, C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001); C. Wunderlich, in Laser<br />
Physics at the Limit (Springer, Heidelberg, 2002), p. 261, arXiv:0111158v1 [quant-ph]; C.<br />
Wunderlich, C. Balzer, Adv. At., Mol., Opt. Phys. 49, 293, (2003).<br />
[2] M. Johanning, A. Braun, N. Timoney, V. Elman, W. Neuhauser, C. Wunderlich,<br />
arXiv:0801.0078v1 [quant-ph].<br />
[3] S. Groth, P. Krüger, S. Wildermuth, R. Folman, T. Fernholz, J. Schmiedmayer, Appl. Phys.<br />
Lett. 85, 2980(2004).
One-dimensional Coulomb chains at low temperatures<br />
G. De Chiara 1 , S. Fishman 2 , T. Calarco 3 and G. Morigi 1<br />
1 Universitat Autonoma de Barcelona, Bellaterra, Spain<br />
2 Department of Physics, Technion, Haifa, Israel<br />
3 Institute for Quantum Information Processing, University of Ulm, Ulm, Germany<br />
Coulomb crystals are organized structures of charged particles, which interact through<br />
the Coulomb repulsion and arrange in regular patterns at sufficiently low temperatures<br />
in the presence of a confining potential [1]. These potentials are realized by means of<br />
Paul or of Penning traps, and their geometry determines the crystal structure. These<br />
crystals represent a kind of rarefied condensed matter, the inter-particle distance being<br />
of the order of several micrometers, allowing to studying the structure by means of<br />
optical radiation. The crystal shape as well as the number of ions can be controlled by<br />
varying the potential. Several remarkable experiments have reported crystallization of<br />
ion gases in Paul and Penning traps [1].<br />
<strong>Here</strong>, we report on recent works, in which we studied the dynamics, thermodynamics<br />
and mechanical instability of Coulomb chains. Coulomb chains are one-dimensional<br />
structures, obtained by means of strong transverse confinement and that usually consist<br />
of dozens of ions localized along the trap axis. They represent a peculiar crystallized<br />
structure: due to the axial potential the equilibrium charge distribution is not uniform.<br />
This is in contrast to the three-dimensional case, where the density of charges in a<br />
harmonic potential is uniform and, therefore, where the eigenmodes are phononic-like<br />
waves. In the Coulomb chain the non-uniformity of the density of ions combined with<br />
the long-range interaction result in excitations that are fundamentally different from the<br />
phonons in solids and lead to interesting thermodynamic properties. Using these results<br />
we discuss the statistical mechanics of the chain, and derive some thermodynamic<br />
quantities such as the specific heat for which we find a non-extensive behaviour [2].<br />
These results allow us to evaluate the critical aspect ratio between the frequencies of the<br />
transverse and the axial confining potential, which determines the stability of the linear<br />
chain. At this value of the aspect ratio, in fact, the crystal structure undergoes an abrupt<br />
transition from a chain to a zigzag configuration. We study the structural phase<br />
transition in the thermodynamic limit, by developing an analytic theory which describes<br />
the behaviour of the system at the critical point [3]. From symmetry considerations we<br />
conjecture the spontaneous symmetry breaking. Applying Landau theory, we identify<br />
the order parameter with the displacement of the equilibrium position from the trap axis,<br />
while the control parameter can be taken as the transverse frequency when the interparticle<br />
distance is fixed. The soft mode, whose frequency becomes zero at the critical<br />
point, is the transverse mode at the shortest wavelength, the so called zigzag mode. Our<br />
theory is valid at T=0, when the system exhibits long-range order. The results we find<br />
are in agreement with the numerical results reported in [4].<br />
________________<br />
[1] D. H. Dubin and T. M. O’Neil, Rev. Mod. Phys. 71, 87 (1999).<br />
[2] G. Morigi and Sh. Fishman, Phys. Rev. Lett 93, 170602 (2004); Phys. Rev. E 70,<br />
066141 (2004).<br />
[3] Sh. Fishman, G. De Chiara, T. Calarco, G. Morigi, Phys. Rev. B 77, 064111 (2008).<br />
[4] J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993). G. Piacente, I. V. Schweigert, J. J.<br />
Betouras, and F. M. Peeters, Phys. Rev. B 69, 045324 (2004).
Ion transport in a segmented Paul trap<br />
G. Huber, W. Schnitzler, R. Reichle, K. Singer and F. Schmidt-Kaler<br />
Institute for Quantum Information Processing, University of Ulm,<br />
Albert-Einstein-Allee 11, 89069 Ulm, Germany<br />
Segmented linear Paul traps are one of the most promising candidates for the<br />
implementation of scalable quantum computing [1]. One key requirement for scalability<br />
is the ability to split strings of ions and transport ions carrying quantum<br />
information between different regions in a trap, e.g. a storing and a processing unit.<br />
We present a segmented linear Paul trap meeting these requirements. It provides<br />
15 pairs of electrodes generating almost arbitrary potentials along the trap axis<br />
including time dependent transport wells, non-harmonic splitting potentials and<br />
multiple trap configurations.<br />
Single 40 Ca + -ions and strings of ions generated by isotope selective photoionization<br />
are confined in the radio frequency Paul trap, laser cooled and detected by their<br />
fluorescence on a CCD camera. Both radial and axial trap frequencies have been<br />
measured and agree with predicted values from numerical calculations with the<br />
precision of a few percent – a necessity for tailoring manipulation potentials. By<br />
applying time dependent voltages [2] to the 15 segment pairs we are able to control<br />
the ion positions over macroscopic distances in a deterministic way, thus splitting and<br />
merging ion chains and transporting single ions over a distance of several millimeters<br />
without loss with a success probability over 99.8%.<br />
References<br />
[1] D. Kielpinsky et al. Nature 417, 709 (2002).<br />
[2] G. Huber et al. New J. Phys. 10, 013004 (2008).<br />
1
Cryogenic Electron-Ion Trap<br />
M. Jilek, T. Kotrík, M. Hejduk, P. Dohnal, I. Korolov, R. Plašil, J.Glosík (*)<br />
Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic<br />
(*) juraj.glosik@mff.cuni.cz<br />
For study of electron-ion recombination and electron attachment at cryogenic collision<br />
energies (down to 10 K) we are constructing electron-ion trap.<br />
The electron trap will use electrostatic field and magnetic field from permanent magnets<br />
for confinement of electrons (using strong gradient of magnetic field - magnetic mirror<br />
like). FEMM (Finite Element Method Magnetic) program is used to model magnetic field<br />
in the trap. The trap is axially symmetric. The calculations were confirmed by<br />
measurement of the magnetic field in the prototype of the trap.<br />
Trapped electrons will be cooled by collisions with Helium buffer gas. The density of<br />
electrons will be roughly 10 7 cm -3 , i.e. high enough to form 3-dimensional potential<br />
minimum on the axis of the trap. The ions formed in external ion source will be trapped<br />
in three dimensional potential minimum created by electrodes and trapped electrons (sort<br />
of nested trap). The trapped plasma will be cooled by elastic collisions with cold helium<br />
(or hydrogen) buffer gas. PIC calculations of electron injection, trapping, confinement<br />
and cooling are carried out and the results will be presented. The electron and ion<br />
trapping and cooling were simulated using code XOOPIC code. Calculated configuration<br />
of magnetic field is used in the XOOPIC calculations.<br />
In the calculation 2×10 7 electrons and 1×10 5 ions are injected into the trap and time<br />
evolution of the plasma cloud is calculated. Helium buffer fills center of the trap.<br />
Presented will be the design and construction of the trap.<br />
In the experiment the decay of the ion density due to recombination with electrons will be<br />
monitored and recombination rate coefficient will be obtained. Low temperature and<br />
relatively high density of electrons can open possibility for study of Collisional radiative<br />
recombination, which has rate proportional to T -4.5 , so it can be at 10 K very fast and<br />
competitive to dissociative recombination.<br />
Acknowledgements: This work is a part of the research plan MSM 0021620834 financed by the<br />
Ministry of Education of the Czech Republic and was partly supported by GACR (202/08/H057,<br />
202/07/0495) by GAUK 53607 and GAUK 124707.
A LINEAR PAUL TRAP FOR ION SPIN MOLECULES<br />
A. Khromova 1 , A. Varon 1 , B. Scharfenberger 1 , Ch. Piltz 1 , Ch. Wunderlich 1<br />
1 Fachbereich Physik, University of Siegen, Walter-Flex Str.3, 57072 Siegen, Germany<br />
Individual atomic ions confined in an electrodynamic cage are a promising system for various<br />
tasks in quantum information science and related fields [1]. In particular, a system of pair-wise<br />
coupled individually accessible spins is useful for experimentally investigating a wide range of topics<br />
in physics. We work on the implementation of a pseudo-spin many-body system, an “ion spin<br />
molecule”, that is, a string of laser cooled atomic ions confined in an electrodynamic trap that is<br />
modified such that an adjustable spin-spin coupling between ions is induced [2]. This will allow for<br />
the well controlled generation and analysis of a large entangled spin system. Examples where this will<br />
be useful include: testing new methods for determining efficiently the entanglement of a many body<br />
system, investigating the decoherence properties of such systems, exploring quantum simulations, or<br />
implementing a neural network.<br />
The current state of our experimental setup will be reported: new linear ion trap, vacuum<br />
chamber organization, laser systems and wavelength meter. The new linear ion tarp was built. SmCo<br />
permanent magnets were added to the design. With the help of them a magnetic field gradient of<br />
20T/m is expected. The ions used in our experiment are 171 Yb + and 172 Yb + . For 171 Yb + experiment<br />
microwave antenna was proposed which will deliver higher magnetic fields into the trap centre. It<br />
makes it possible to control as well which transition of the hyperfine levels we would like to excite.<br />
Light at 369nm and 935nm is used to perform the cooling cycle together with the microwave<br />
source for 171 Yb + . Another two wavelength used in our experiment are 399nm for photoionization and<br />
638nm for repumping the metastable state F 7/2 . All four wavelengths are produced by diode laser<br />
systems frequency stabilized using side-of-fringe frequency stabilization. The general frequency<br />
control scheme will be demonstrated.<br />
For precise measurements of the lasers’ wavelengths the wavelength meter was designed. It is<br />
based on the Michelson interferometer. As a reference frequency, used for locking, the cross-over<br />
signal (linewidth ~6MHz) of the 5 2 P 3/2 , F=3 ↔ 5 2 S 1/2 , F=2 transition in the Rubidium atom is used.<br />
Light at 780,027nm (D2 transition) is produced by a diode laser. The details of the construction will be<br />
highlighted.<br />
[1] J.I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); D. Leibfried et al., Nature 438, 639<br />
(2005); H.Häffner et al., Nature 438, 643 (2005)<br />
[2] Ch.Wunderlich, Conditional Spin Resonance with Trapped Ions, Laser Physics at the Limits,<br />
p.261, (Springer, 2002); Ch.Wunderlich and Ch.Balzer, Adv. At. Mol. Opt. Phys. 49, 295 (2003)
High fidelity quantum gates with trapped 43 Ca + ions.<br />
G. Kirchmair 1,2 , J. Benhelm 1,2 , F. Zähringer 1,2 , R. Gerritsma 1,2 , C. F. Roos 1,2 , and R. Blatt 1,2<br />
1 Institut für Experimentalphysik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria<br />
2 Institut für Quantenoptik und Quanteninformation,<br />
ÖAW, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria<br />
For fault-tolerant computation, it is commonly believed that error thresholds ranging<br />
between 10 −4 and 10 −4 will be required depending on the noise model and the computational<br />
overhead for realizing the quantum gates. Up to now, all experimental implementations have<br />
fallen short of these requirements.<br />
I report on a Mølmer-Sørensen type gate operation entangling states with a fidelity of<br />
99.3% which together with single-qubit operations forms an universal set of quantum gates.<br />
The gate operation is performed on a pair of qubits encoded in two trapped calcium ions using<br />
a single amplitude-modulated laser beam interacting with both ions at the same time. A<br />
robust gate operation, mapping separable states onto maximally entangled states, is achieved<br />
by adiabatically switching on and off the laser-ion coupling. We analyse the performance of<br />
a single gate and concatenations of up to 21 gate operations.
Study of ion dynamics in a radiofrequency trap<br />
by molecular dynamics simulations<br />
Mathieu Marciante, Annette Calisti, Caroline Champenois, Martina Knoop, Fernande Vedel<br />
Physique des Interactions Ioniques et Moléculaires (CNRS UMR6633),<br />
Université de Provence, Centre de Saint Jérôme, case C21, Marseille cedex 20, France<br />
Molecular Dynamics simulations are carried out to evaluate the general behaviour of the<br />
dynamics of ions in a radiofrequency trap. We present the different types of motion allowed<br />
by this kind of device for a single ion and compare it with the secular approximation that can<br />
be done, finding thus the limits of this approximation. Single ions can be followed in a small<br />
ion cloud allowing to evidence the mobility in the Coulomb crystal for different pseudopotentiel<br />
well depths (figure).<br />
Figure: Projection of the motion of 40 Ca + ions for two different pseudopotential well depths<br />
(V AC =800V, Ω/2π=10 MHz, above U DC =0V, below U DC =4V), blue points. Green points follow the motion<br />
of a single ion during 2000 rf periods. Left: x-y, centre: x-z, right: symmetry of the potential well depth<br />
We then illustrate some periodic and chaotic trajectories by analyzing the dimensionless<br />
Poincaré section of our system. We present the structures of a thermalized ion cloud for<br />
different values of the confinement parameters and the organization of a two-species ion<br />
cloud. These structures are finally used to simulate the observations carried out by a CCD<br />
camera.<br />
At present simulations are extended to different confinement potentials in a linear<br />
configuration, in particular octupole [1] and dodecapole trap, where the dynamics of a large<br />
ion cloud will be studied experimentally.<br />
[1] K. Okada, K. Yasuda, T. Takayanagi, M. Wada, H.A. Schuessler, S. Ohtani, Crystallization of Ca +<br />
ions in a linear rf octupole ion trap, Phys. Rev. A 75, 033409 (2007)
A planar Paul trap<br />
Robert Matjeschk<br />
An approach to investigate the dynamics of quantum many-body systems<br />
is quantum simulations. A promising realisation is the simulation based on<br />
ions in Paul traps. Besides the principle study of feasibility, an important<br />
issue is scalability - the possibility to confine and control many ions. Quantum<br />
simulations using an order of 10x10 ions - still a challenging dream - are<br />
supposed to lead to new insight into quantum many-body dynamics.<br />
In linear traps this scalability is hindered by the fact that all ions are<br />
trapped in one effective oscillator potential. This leads for example to a<br />
non-homogeneous distance distribution and thus to a non-homogeneous interaction<br />
strength distribution between the ions.<br />
Our group has successfully simulated a quantum magnet consisting of<br />
two interacting spins using ions in a linear Paul trap [1]. Increasing the spinspin<br />
interaction adiabatically from zero to a specific (large) value led to a<br />
transition from a paramagnetic to a ferromagnetic state with a probability of<br />
98 %. We were able to prove, that with a fidelity of 88 % the system evolved<br />
into a superposition state | ↑↑〉+| ↓↓〉, being equivalent to an entangled state.<br />
To be able to address more complex systems, we are developing a 2Dsurface-trap<br />
where four ions will be arranged in a two-dimensional plane.<br />
Each ion will be confined in its own effective oscillator potential, while the<br />
(homogeneous) distance between the ions is still small enough (about 20<br />
µm) to maintain a non-negligible ion-ion interaction (mediated by coulomb<br />
forces). Such a trap design should in principle be scalable.<br />
[1] to be published (see arxiv 0802.4072v2)<br />
1
Multipolar trap geometries for particle trapping under standard<br />
reference temperature and pressure conditions<br />
B. M. Mihalcea, O. S. Stoican, Gina T. Vişan, L. M. Dincă and I. N. Mihăilescu<br />
National Institute for Laser, Plasma and Radiation Physics (INFLPR), Bucharest-Măgurele, Romania<br />
E-mail: bmihal@infim.ro; stoican@infim.ro<br />
Generation of nonlinear states (especially entangled states) in ion traps [1] increases the<br />
signal-to-noise ratio in spectroscopy and will enable future implementation of quantum logic [2]<br />
as well as future progress on the realization of very high accuracy atomic clocks. That is why<br />
current interest is centered on minimizing the perturbing mechanisms associated to the trapping<br />
phenomenon, such as the second order Doppler shift, decoherence mechanisms, etc. We have<br />
designed and tested new linear multipolar trap geometries, operating in air, under standard<br />
temperature and pressure reference conditions [3]. Our main interest was focused on illustrating<br />
the trapping phenomenon for such trap geometries and study microparticle dynamics. After<br />
testing different geometries and geometrical configurations, we have investigated an octupole<br />
trap geometry and a dodecapole trap geometry, presented in Fig. 1 and Fig. 2. The trap<br />
electrodes, equidistantly spaced, are made of brass. An electronic system which we designed is<br />
used in order to generate the trapping voltages, as well as the voltage used for particle diagnosis.<br />
We have generated microplasmas and investigated the ordering conditions for different trapping<br />
parameters, using microparticle species such as SiC and Al 2 O 3 . The two traps are currently<br />
undergoing tests in our group and a numerical simulation on the particle dynamics is approached.<br />
Figure 1: octupole trap geometry<br />
Figure 2: dodecapole trap geometry<br />
References<br />
[1] P. K. Ghosh, Ion Traps, Clarendon Press, Oxford (1995)<br />
[2] I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)<br />
[3] O. S. Stoican, B. M. Mihalcea, L. C. Giurgiu, and I. N. Mihăilescu, Satellite Meeting Atomic<br />
Physics with Trapped Ions, 23-24 July 2006, Innsbruck, Book of abstracts, P43 (2006)
Michael Niedermayr<br />
Universität Innsbruck – Institut für Experimentalphysik<br />
Towards Cryogenic Surface Ion Traps<br />
One promising approach for scalable quantum information processing (QIP) architectures is<br />
based on miniaturized surface ion traps [1]. These traps with dimensions in the sub-100µm<br />
range can be fabricated by photolithography techniques [2]. Generally, experimental results<br />
indicate that the heating rate of the ions increases with decreasing trap dimensions.<br />
The mechanism of this heating is not yet fully understood. However, the heating rate can be<br />
reduced by several orders of magnitude when the trap electrodes are cooled from room<br />
temperature to 4K [3, 4].<br />
Within a new experiment which is presently set up we intend to investigate surface traps at<br />
low temperatures in a cryogenic system. These traps will be applied for quantum simulations,<br />
for fundamental investigations of large-scale entanglement and for precision measurements<br />
enhanced by quantum metrology techniques employing entangled particles.<br />
[1] D. Kielpinski et al., Nature 417, 709 (2002)<br />
[2] J. Chiaverini et al., Quantum Inf. Comput. 5, 419 (2005)<br />
[3] J. Labaziewicz et al., Phys. Rev. Lett. 100, 013001 (2008)<br />
[4] L. Deslauriers et al., Phys. Rev. Lett. 97, 103007 (2006)
Experimental demonstration of a deterministic single ion source with an<br />
expected implantation resolution of a few nm<br />
W. SCHNITZLER, N. M. LINKE, J. EBLE, F. SCHMIDT-KALER, and K. SINGER –<br />
Universität Ulm, Institut für Quanteninformationsverarbeitung, Albert-Einstein-Allee 11,<br />
89069 Ulm, Germany<br />
We have realized a universal deterministic single ion source on the basis of an ion trap<br />
applicable to a wide range of elements and molecules [1]. Initially, cold 40 Ca + ion crystals are<br />
trapped within a segmented linear trap. Those ions are then deterministically extracted and<br />
shot into a detector at a distance of 25 cm from the trap. With single ions, more than 90% of<br />
these extractions were successful. The kinetic energy distribution of the ions amounts to less<br />
than 0.1%. We have also demonstrated the extraction of mixed ion crystals containing other<br />
dopant ions.<br />
For the implantation with nm precision, we plan to utilize an electrostatic Einzel-lens to<br />
further improve the spatial resolution of the extracted ions. These can then be used to generate<br />
color centers in diamond for optical detection or to implant P into Si. Both systems provide<br />
the foundation for the realization of a solid state quantum computer [2,3]. In addition, the<br />
electrical properties of semiconductor devices can be greatly enhanced by the deterministic<br />
implantation of single ions [4].<br />
[1] J. Meijer et. al., Appl. Phys. A 83, 321 (2006)<br />
[2] F. Jelezko et. al., Phys. Rev. Lett. 93, 130501 (2004)<br />
[3] B. E. Kane, Nature 393, 133 (1998)<br />
[4] T. Shinada et. al., Nature 437, 1128 (2005)
Acoustic excitation of the charged microparticles motion in a linear<br />
electrodynamic trap<br />
O. S. Stoican, B. Mihalcea, L. Dinca, G. Visan<br />
INFLPR, 409Atomistilor St., Magurele, 077125 Romania<br />
stoican@infim.ro<br />
An experimental study on the interaction between an acoustic wave and the charged<br />
microparticles stored in a linear electrodynamic trap is presented. The linear<br />
electrodynamic trap consists of four bar electrodes equidistantly spaced, supplied by a<br />
high ac voltage Vcos2πft, and two endcap disc electrodes. A dc voltage applied to the<br />
endcap electrodes assures the axial stability of the stored particles. The microparticles<br />
consisting of Al 2 O 3 powder, 63-200 μm in diameter, have been stored in air at normal<br />
pressure. The output beam of a low power laser module is focused on the longitudinal<br />
axis of the linear trap where the density of the stored microparticles has a maximum<br />
value. A fraction of the radiation scattered by the stored microparticles is received by an<br />
integrated photodetector, directed normal to the linear trap axis, and converted into an<br />
electrical voltage. The motion of the stored particles modulates the intensity of the<br />
scattered radiation so that photodetector output voltage has the same harmonic<br />
components. One of the dominant harmonics is due to the so-called “micromotion” at<br />
frequency f of the ac supply voltage. The amplitude A(f) of the photodetector output<br />
voltage harmonic component at frequency f is measured using a synchronous detection<br />
technique. Supplementary force field acting on the stored microparticles is produced<br />
using an acoustic wave generated by a loudspeaker. Effects of the acoustic wave are<br />
studied observing the time variation of the amplitude A(f). The beat oscillations due to the<br />
action of the acoustic wave have been evidenced. Because the action of the acoustic wave<br />
is purely mechanical this experimental approach allows decoupling the mass m and the<br />
electric charge q, respectively, from equation of motion of the stored microparticles.<br />
Results are discussed.
Design and Characterization of a Planar Trap<br />
U. Tanaka 1, 2 , R. Naka 1 , F. Iwata 1 , T. Ujimaru 1 , K. R. Brown 3 , I. L. Chuang 4 and S. Urabe 1, 2<br />
1 Graduate School of Engineering Science, Osaka University, Japan, 2 JST-CREST, Japan<br />
3 School of Chemistry and Biochemistry, Division of Computational Science and Engineering,<br />
Georgia Institute of Technology, USA<br />
4 Center for Bits and Atoms and Department of Physics, Massachusetts Institute of Technology, USA<br />
Planar traps [1-4] have substantial potential for realizing large-scale quantum information<br />
processing such as quantum CCD [5] since its structure is suitable for fabrication of complicated<br />
geometries. We report experiments of 40 Ca + ions with a planar trap whose layout of electrodes is<br />
shown in Fig. 1. It is made of a low-rf-loss substrate and deposited with copper. The potential<br />
minimum is estimated to be located about 0.8 mm above the surface of the center electrode and the<br />
typical potential depth is about 1 eV. Calcium ions are loaded by two-step photo-ionization using a<br />
423 nm diode laser for the 4s 2 1 S 0 - 4s4p 1 P 1 transition and a light emitting diode for the second<br />
excitation [6]. Laser cooling and detection of ions are performed with the 4s 2 S 1/2 - 4p 2 P 1/2 transition<br />
at 397 nm and the 4p 2 P 1/2 - 3d 2 D 3/2 transition at 866 nm. Laser beams that are parallel to the trap<br />
surface are irradiated as shown in Fig. 1.<br />
We measured the motional frequencies of ions and compared them to those estimated by<br />
simulation. Brief micromotion compensation was performed in the x-z plane by varying the DC<br />
voltages with monitoring fluorescence spectra. Figure 2 shows an image of two 40 Ca + ions aligned in<br />
the z direction.<br />
We also discuss miniaturization of the trap and other designs and show simulated results.<br />
Laser beam<br />
(397 nm)<br />
End electrode<br />
DC electrodes<br />
End electrode<br />
x<br />
z<br />
Laser beams<br />
(397 nm, 866 nm,<br />
423 nm)<br />
RF electrode<br />
Center electrode<br />
1.5mm<br />
End electrode DC electrodes End electrode<br />
Fig. 1<br />
Layout of trap electrodes.<br />
10m<br />
Fig. 2 Two 40 Ca + ions confined in the planar trap.<br />
[1] J. Chiaverini et al., Quantum Inf.Comput. 5, 419-439 (2005)<br />
[2] C. E. Pearson et al., Phys. Rev. A 73, 032307 (2006)<br />
[3] S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006)<br />
[4] Kenneth R. Brown et al., Phys. Rev. A 75, 015401 (2007)<br />
[5] D. Kielpinski et al. Nature 417, 709 - 711 (2002)<br />
[6] U. Tanaka et al. Appl. Phys. B 81, 795-799 (2005)
Sideband cooling and coherent dynamics<br />
in a microchip multi-segmented ion trap<br />
Contribution 1<br />
St. Schulz 1 , U. Poschinger 1 , F. Ziesel 1 , G. Huber 1 , F. Schmidt-Kaler 1<br />
1 Universität Ulm, Institut für Quanteninformationsverarbeitung,<br />
Albert-Einstein-Allee 11, 89069 Ulm, Germany<br />
Miniaturized multi-segmented linear ion traps are a promising architecture for<br />
quantum information processing in a scalable way [1]. The miniaturization of linear<br />
Paul traps allows partitioning the trap region in storage and processing regions<br />
for qubits. The individual control of many qubits in different adjacent zones is<br />
fundamental for the implementation of large-scaled quantum algorithms. The crucial<br />
requirement for a scalable quantum processor is the fast qubit transport between<br />
spatial separated trap regions.<br />
We present a novel scalable microchip multi-segmented ion trap with two different<br />
adjacent zones, one for the storage and another dedicated for the processing<br />
of quantum information using single ions and linear ion crystals: A pair of radiofrequency<br />
driven electrodes and 62 independently controlled DC electrodes allow<br />
shuttling of single ions or linear ion crystals with numerically designed axial potentials<br />
at axial and radial trap frequencies of a few MHz [2]. We characterize the trap<br />
using sideband spectroscopy on the narrow S 1/2 ↔ D 5/2 transition of the 40 Ca + ion,<br />
demonstrate coherent Rabi rotations, Ramsey spectroscopy, optical ground state<br />
cooling and determine the heating rate [3].<br />
Recently we succeeded in combining sideband spectroscopy with a single ion transport<br />
along the trap axis: Initially held and Doppler cooled in the loading region, the<br />
ion is shuttled to a different trap region where we perform sideband spectroscopy.<br />
Shuttled back, we reveal the ions quantum state from a fluorescence measurement.<br />
Such operations are necessary for subsequent two-qubit quantum logic operations.<br />
The applicability of our trap for scalable quantum information processing is proven.<br />
References<br />
[1] Kielpinski et al., Nature 417, 709 (2002).<br />
[2] Schulz et al., Fortschr. Phys. 54, 648 (2006).<br />
[3] Schulz et al., NJP, in press April 2008.<br />
1
Controlling the Motion of Small Numbers of Ions in a Penning Trap<br />
D. Crick, S. Donnellan, H. Ohadi, I. Bhatti, R.C. Thompson and D.M. Segal,<br />
Imperial College London<br />
We are studying Ca + ions held in a Penning trap with a view to applications in<br />
quantum information processing (QIP) and the study of quantum mechanical phase<br />
transitions. Results demonstrating laser cooling and observation of individual calcium<br />
ions in a Penning trap will be presented. We have previously suggested a scalable<br />
approach to QIP using ions in multiple miniature Penning traps, which involves<br />
moving ions from one trap to another in a controlled manner [1]. The traps involved<br />
are made by depositing arrays of ‘pad’ electrodes onto a pair of opposing planar<br />
substrates. We report the design, construction and operation of a prototype array, with<br />
three trapping zones, made from vacuum compatible circuit board. The next step is to<br />
demonstrate the controlled movement of ions between the traps. Of relevance to<br />
future work on quantum phase transitions we also report recent work with small<br />
numbers of ions held in a conventional 3D Penning trap. We show that we are able to<br />
trap, cool, image and manipulate the shape of very small ensembles of ions<br />
sufficiently well to produce two-ion ‘Coulomb crystals’ aligned along the magnetic<br />
field of a Penning trap. Images are presented which show the individual ions to be<br />
resolved in a two-ion ‘crystal’. A distinct change in the configuration of such a<br />
structure is observed as the experimental parameters are changed [2].<br />
[1] J. R. Castrej´on-Pita, H. Ohadi, D. R. Crick, D. F. A. Winters, D. M. Segal, and R.<br />
C. Thompson. ‘Novel Designs for Penning Ion traps’. J. Mod. Opt. 54, 1581–1594,<br />
2007.<br />
[2] D. R. Crick, H. Ohadi, I. Bhatti, R. C. Thompson, and D. M. Segal. ‘Two-ion<br />
Coulomb crystals of Ca + in a Penning trap’, Optics Express, Vol. 16, Issue 4, pp.<br />
2351-2362 (2008).
QUANTUM INFORMATION
Quantum information with Strontium ions at the Weizmann Institute<br />
Nitzan Akerman, Shlomi Kotler and Roee Ozeri<br />
The Weizmann institute of science, physics of complex system department<br />
Rehovot, Israel.<br />
Abstract<br />
We at the Weizmann institute, Israel, are engaged in the construction of a new ions<br />
trapping lab for quantum information experiments. We are using Strontium 88 atoms<br />
which are ionized by two stage photonionization scheme and trapped using a linear<br />
Paul trap made of tungsten needles. Since 88 Sr has no nuclear spin, the qubit will be<br />
encoded into the Zeeman levels of the 5S 1/2 manifold. Due to the qubit sensitivity to<br />
magnetic noise, an active feedback system is applied to compensate for such noise to<br />
the micro Gauss regime (@50Hz). The detection of up/down state is aided by a<br />
shelving scheme into the D5/2 using a narrow width (sub kilohertz) laser, to be<br />
constructed.
Cavity QED and Cavity Mediated Cooling Using Ion<br />
Coulomb Crystals<br />
M.Albert, J.P.Marler, P.F.Herskind,A.Dantan,<br />
M.B.Langkilde-Lauesen and M.Drewsen<br />
Institute of Physics and Astronomy, University of Aarhus,<br />
Ny Munkegade, Building 520, DK-8000 Aarhus C, Denmark<br />
E-mail: malbert@ifa.au.dk<br />
Clouds of cold ions represent an interesting alternative system to a single<br />
atom/ion for studying CQED effects. When a trapped cloud of ions is cooled<br />
below a certain critical temperature (≈mK), the ions form a spatially ordered<br />
state, refered to as an ion Coulomb crystal.<br />
These ion Coulomb crystals can be easily trapped and cooled in sufficient<br />
number to potentially access the interesting regime where the cooperativity<br />
parameter, C = g2 N<br />
, is greater then one and the collective coupling g√ N<br />
2κγ<br />
exceeds both the spontaneous decay rate, 2γ, and the cavity decay rate,<br />
κ, without using extremely high finesse cavities (g is the single atom-field<br />
coupling parameter, N the number of atoms in the cavity mode).<br />
In our setup, photoionisation allows the controlled isotope selective loading<br />
of ion Coulomb crystals of arbitrary size (10-10000 ions) into a linear Paul<br />
trap. Our high finesse cavity (κ ≈ 2 MHz) is mounted co-linear with the trap<br />
axis and provides good overlap of the cavity mode with the Coulomb crystal.<br />
We will present recent experimental results which indicate that the number of<br />
40 Ca + ions inside the cavity mode of our experimental setup is high enough<br />
to achieve strong collective coupling, together with the first indications of<br />
collective coupling of the ion Coulomb crystal to the cavity field.<br />
Beside near-future CQED experiments, opportunities to use our system to<br />
further cool the ion crystals by cavity mediated cooling schemes are discussed.<br />
1
The Dirac Equation in Trapped ions<br />
A. Bermudez<br />
Departamento de Física Teórica I, Universidad Complutense, 28040. Madrid, Spain.<br />
We develop a novel quantum optical perspective into a couple of quantum relativistic systems: First we show<br />
how the two-dimensional extension of the harmonic oscillator, known as the Dirac oscillator, can be exactly mapped<br />
onto a chiral Anti-Jaynes-Cummings model of quantum optics. This equivalence allows us to predict a series of<br />
novel relativistic phenomena, such as spin-orbit Zitterbewegung. Furthermore, we also make a realistic experimental<br />
proposal, at reach with current technology, for studying the equivalence of both models using a single trapped ion<br />
[1]. Second, we show that a relativistic version of Schrödinger cat states, here called Dirac cat states, can be built in<br />
relativistic Landau levels when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under<br />
suitable initial conditions, the associated Dirac equation produces unitarily Dirac cat states involving the orbital<br />
quanta of the particle in a well defined mesoscopic regime. These states have a purely relativistic origin and cease to<br />
exist in the non-relativistic limit [2].<br />
[1] A. Bermudez , M. A. Martin-Delgado, E.Solano, Phys. Rev. A. 76, 041801(R) (2007).<br />
[2] A. Bermudez, M. A. Martin-Delgado, E.Solano, Phys. Rev. Lett. 99, 123602 (2007)
Generation of relative-intensity squeezed light using four-wave mixing<br />
in an rubidium atomic vapor<br />
Q. Glorieux, ∗ R. Dubessy, B. Dubost, S. Removille, T. Coudreau,<br />
S. Guibal, L. Guidoni, J.P. Likformann, and N. Sangouard<br />
<strong>Laboratoire</strong> Matériaux et Phénomènes Quantiques,<br />
CNRS UMR 7162 et Université Denis Diderot, Paris<br />
P. Milman<br />
<strong>Laboratoire</strong> de PhotoPhysique Moléculaire du CNRS, Université Paris-Sud XI<br />
In order to test a quantum memory in the continuous variables regime, based on trapped Sr +<br />
ions, we have started an experiment to produce relative-intensity squeezed light. We plan to store<br />
the information contained in the quadratures of light beams on the quadratures of an observable of<br />
an ensemble of ions. In particular, we plan to use non classical states (intensity correlated beams) [1].<br />
Four-wave mixing (4WM) is one among the different technique used to produce quantum correlated<br />
beam. The advantages of this technique are the large level of squeezing possible, and the simplicity<br />
of the set-up compared to OPOs based methods. We are starting an experiment based on the work of<br />
[2] who have obtained 8dB of relative-intensity squeezing at 795nm in a vapor of rubidium atoms. We<br />
are also working on a model based upon the Heisenberg-Langevin approach [3] to find the optimal<br />
parameters.<br />
For our application with an ion cloud of Sr + , we need to transpose this experiment to S 1/2 → P 1/2<br />
transition at 422nm. Hopefully, rubidium has an atomic transition at a wavelength close to the one<br />
of Sr + , and we will be able to use a rubidium atomic vapor to produce relative-intensity squeezed<br />
beams at 422nm.<br />
We describe in the poster the experimental setup, our first results at 795nm and summarize our<br />
theoretical developments.<br />
[1] T. Coudreau, F. Grosshans, S. Guibal, L. Guidoni, Feasibility of a quantum memory for<br />
continuous variables based on trapped ions : from generic criteria to practical implementation.<br />
J. Phys. B : At. Mol. Opt. Phys., vol. 40 (2) pp. 413-426 (2007)<br />
[2] C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, Strong relative intensity squeezing by four-wave<br />
mixing in rubidium vapor for light, Opt. Lett. 32, 178-180 (2007)<br />
[3] L. Davidovich Sub-Poissonian process in quantum optics Rev. Mod. Phys., Vol 68, No 1, (January 1996)<br />
∗ Electronic address: quentin.glorieux@univ-paris-diderot.fr
From a single-photon emitter to a single ion laser<br />
Authors: Helena G. Barros 1,2 , François Dubin 1 , Carlos Russo 1,2 , Andreas Stute 1,2 , Piet O.<br />
Schmidt 1 , and Rainer Blatt 1,2 — 1 Institut für Experimentalphysik, Universiät Innsbruck,<br />
Technikerstr. 25, A-6020 Innsbruck — 2 Institut für Quantenoptik und Quanteninformation,<br />
Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck<br />
A single atom interacting with a single mode of a cavity is the building block of a laser<br />
from a fundamental point of view. In this work, we study a single 40 Ca + ion coupled to a high<br />
finesse optical resonator. In particular, we evaluate the statistical properties of emitted cavity<br />
photons for different regimes of operation.<br />
In the experiment, a drive laser together with an optical cavity excites an off-resonant<br />
Raman transition that connects the S 1/2 and D 3/2 levels of the 40 Ca + ion. Population gets<br />
transferred from S 1/2 to D 3/2 while emitting a photon into the cavity. The excitation cycle is<br />
closed by a recycling laser that brings the atomic population back to the initial state S 1/2 via<br />
resonant excitation of the P 1/2 state. The photons leave the cavity at a rate of 54 kHz and are<br />
sent to a Hanbury-Brown & Twiss setup, where photon-photon correlations are measured. For<br />
weak recycling laser intensity, the system is operating as a single-photon source. In this<br />
regime, we can tune the statistics of the photon arrival times from sub-Poissonian to super-<br />
Poissonian behaviour. For faster recycling rates, we observe a single-atom laser at threshold.
Quantum phases of the frustrated nearest-neighbor XY<br />
model on the anisotropic triangular lattice<br />
P. Hauke, R. Schmied, T. Roscilde, V. Murg, D. Porras, and J. I. Cirac<br />
With the help of exact diagonalization, projected entangled pair states (PEPS),<br />
spin wave, and modied spin wave theory we analyze the ground state of the frustrated<br />
nearest-neighbor XY model on the anisotropic triangular lattice [1]. As<br />
summarized in the gure below, we nd that the transition from the 1D gapless<br />
spin-liquid phase to the 2D spiraling ordered phase passes through a gapped<br />
spin-liquid phase, similar to what has been predicted for the same model with<br />
Heisenberg interactions [2]. Further, a second gapped spin-liquid phase marks the<br />
transition to the 2D Néel-ordered phase. We propose that the evolution from a<br />
1D gapless spin liquid to a spiraling ordered state, and from spiral to Néel order,<br />
acquires a `universal' discontinuous structure: instead of a continuous deformation<br />
of correlations in the ground state, exhibited by the classical system, the quantum<br />
system rst shows a complete loss of (quasi-)long-range correlations in favor of<br />
a short-range spin-liquid state, and then a revival of correlations at a dierent<br />
wavevector.<br />
We propose a setup for quantum simulation of this frustrated nearest-neighbor<br />
XY model on the anisotropic triangular lattice. The vibrational degrees of freedom<br />
of trapped ions may be mapped to a spin-1/2 system due to the strong<br />
anharmonicity induced by an optical lattice potential. These eective spins couple<br />
via the dipoledipole component of the Coulomb interaction between the ions,<br />
which falls o as the third power of distance. By adjusting the spatial direction<br />
of vibration, the anisotropy of the dipoledipole interaction can be tuned over a<br />
sucient range. This scheme may easily be extended to other geometries.<br />
references:<br />
[1] R. Schmied, T. Roscilde, V.<br />
Murg, D. Porras, and J. I. Cirac,<br />
arXiv:0712.4073v2 [cond-mat.str-el]<br />
[2] S. Yunoki and S. Sorella, Phys. Rev.<br />
B 74 014408 (2006)<br />
1
Trapped Ion Cavity-QED:<br />
Interfacing Ions and Photons<br />
P. Blythe, A. Mortensen, N. Seymour-Smith, M. Keller and W. Lange<br />
University of Sussex<br />
Miniature cavity-QED systems are a versatile tool for many applications<br />
in quantum information processing, ranging from the exchange of quantum<br />
informations between nodes of a quantum network to the entanglement of<br />
multiple atoms by means of intra-cavity photon exchange. We investigate<br />
different schemes taking advantage of the precise control of the ions’ motional<br />
and internal degrees of freedom.<br />
Deterministic entanglement of ions and photons and the mapping of their<br />
respective quantum states allows for a bidirectional transfer of quantum information<br />
over long distances. A crucial element in such a transfer is the<br />
deterministic generation of single photons from a single atom, which we have<br />
achieved using a 40 Ca + -ion stored in a radio-frequency trap in the Lamb-<br />
Dicke regime. As we have demonstrated, single photons can be extracted<br />
from the ion continuously over times on the order of hours. We have recently<br />
improved our set-up by implementing a novel miniature ion-trap system allowing<br />
for much shorter cavities. This enhances the coherent coupling between<br />
the ion and the cavity mode, reaching the regime of strong coupling.<br />
The trap comprises three sandwiched layers of copper electrodes, insulated<br />
by kapton spacers. Optimal alignment is provided by machining each layer<br />
from a single sheet, separating the individual electrodes after fixing their position.<br />
Apart from deterministic schemes we are also investigating probabilistic entanglement<br />
methods. We have developed a scheme to entangle two ions coupled<br />
to the same cavity by detecting two coincident photons emitted from<br />
the cavity with orthogonal polarisation. In this case, the constraints on the<br />
coherent coupling are more relaxed and therefore larger cavities can be used.<br />
We have developed an ion-trap cavity system which is especially suited for<br />
this application.
Towards a Quantum memory in trapped ions<br />
S. Removille, ∗ R. Dubessy, Q. Glorieux, T. Coudreau, S.<br />
Guibal, L. Guidoni, J.P. Likforman, and N. Sangouard<br />
<strong>Laboratoire</strong> Matériaux et Phénomènes Quantiques,<br />
CNRS UMR 7162 et Université Denis Diderot, Paris<br />
Trapped ions constitute a choice material for quantum information, and in particular for the realization<br />
of quantum memories. Such a memory will be of particular importance in order to implement<br />
long-distance quantum communication networks.<br />
Quantum information can be stored and manipulated in systems containing a small number of<br />
particles (discrete variables regime) as well as in much larger systems (continuous variables regime).<br />
In the continuous variables regime, one seeks to store the information contained in the quadratures<br />
of a polarized light beam on the observables defined on an ensemble of atoms or ions. This has already<br />
been achieved using a cloud of cesium atoms at room temperature [1]. However important issues have<br />
still to be reached such as increasing the storage time which is now on the order of the millisecond. We<br />
have shown that one can in principle implement with trapped and cooled ions a quantum memory<br />
which allows for the a posteriori measurement of an arbitrary quadrature with storage times of<br />
several seconds [2]. These long storage times can be explained by the absence of the most common<br />
sources of decoherence, namely collisions, finite interaction time and dephasing effects due to stray<br />
magnetic fields.<br />
We are developing an experimental setup devoted to store quantum information in a cloud of cold<br />
trapped ions. We have already trapped up to 10 4 Sr + ions in a large linear Paul trap. The ions are<br />
slown down using Doppler laser cooling. We retrieve the fluorescence of the cloud on a CCD camera<br />
and the reached temperature is on the order of 100mK. We have recently settled a photoionisation<br />
system that enables us to load the trap in a low heating rate regime, reaching lower temperatures in<br />
large clouds. We will describe in the poster the experiments carried out to obtain a well controlled<br />
cloud of cold ions.<br />
[1] B. Julsgaard, J. Sherson, J.I Cirac, J. Fiurášek, E.S. Polzik, ”Experimental demonstration of quantum<br />
memory for light”, Nature 432, 482 (2004)<br />
[2] T. Coudreau, F. Grosshans, S. Guibal, L. Guidoni, Feasibility of a quantum memory for continuous<br />
variables based on trapped ions J. Phys. B, 40, 2 (2007)<br />
∗ Electronic address: sebastien.removille@univ-paris-diderot.fr
Towards two-dimensional quantum simulations with trapped ions<br />
Christian Schneider † , Robert Matjeschk, and Tobias Schaetz<br />
Max-Planck-Institut fuer Quantenoptik, Garching, Germany<br />
An ion crystal in a Paul trap is a promising candidate for a quantum simulator or analogue<br />
quantum computer. Thereby a quantum system shall be implemented and studied which is<br />
described by the same Hamiltonian as the system to be simulated. The crucial parameters of<br />
the implemented system are accessible which is often not the case for the “real” sytem. First<br />
experimental results in building a quantum simulator for a Quantum Ising Hamiltonian with<br />
two ions have recently been shown [1].<br />
To gain deeper insight into quantum dynamics, we plan to extend these fundamental experiments<br />
to more ions and into two dimensions [2]. As successful studies of one-dimensional planar<br />
Paul traps have been shown [3,4], a promising approach is to realize a two-dimensional array<br />
of trapped ions in a planar two-dimensional surface trap. We want to show our visions of twodimensional<br />
quantum simulations and first steps towards their realization by a two-dimensional<br />
Paul trap of 2 × 2 ions.<br />
[1] A. Friedenauer, H. Schmitz et al., arXiv 0802.4072v1, 1-6<br />
[2] T. Schaetz et al., J. Mod. Opt. 54, 2317–2325<br />
[3] J. Chiaverini et al., Quant. Inf. Comp. 5, 419–439<br />
[4] S. Seidelin et al., Phys. Rev. Lett. 96, 253003–4<br />
† mailto:christian.schneider@mpq.mpg.de
Trapped Barium Ions for Quantum Computation, Atomic Clock and<br />
Precise Measurement<br />
G.Shu, N.Kurz, M.Dietrich, A.Kleczewski, G.Howell, R.Bowler, J.Salacka, P.Green,<br />
B.B.Blinov<br />
Department of Physics, University of Washington<br />
Abstract<br />
This poster presents the research at University of Washington centered around single trapped<br />
barium ions. Single-ionized odd isotope of barium( 137 Ba + ) is an excellent candidate for hyperfine<br />
qubit. Its ground state splits into two hyperfine levels 8GHz apart with almost infinite<br />
lifetime and long coherence, thus making it an excellent choice for qubit states. We show the<br />
schemes of qubit initialization, detection and manipulation in this poster.<br />
A single photon source based on ultrafast pulse driven Barium ion is also under developing.<br />
Besides simple structure and high repetition rate, it can also bridge the static qubits(ions) with<br />
flying qubits(photons) and make remote entanglement of photons and atoms possible, which is<br />
desirable for quantum computation and communication.<br />
Single Barium ion is also a nice platform for precise atomic measurements and optical clocks.<br />
Efforts are made to build a frequency reference based on 138 Ba + ’s 6S 1/2 ↔ 5D 3/2 dipole forbidden<br />
transition. Besides its extremely narrow natural line width (5D 3/2 ’s lifetime is 80s),<br />
another attractive property is its insensitivity to quadruple electric field which is one of the main<br />
sources of systematic error in a quadruple trap. The progress of this work is also presented in<br />
this poster.<br />
1
Quantum imaging with trapped ions<br />
*J. von Zanthier 1 , Ch. Thiel 1 , Th. Bastin 2 , G. S. Agarwal 3<br />
1<br />
Institut für Optik, Information und Photonik, Universität Erlangen-Nürnberg, Staudtstrasse 7/B 2, D - 91058 Erlangen, Germany<br />
2<br />
Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège au Sart Tilman, Bât. B15, B - 4000 Liège, Belgium<br />
3Department of Physics, Oklahoma State University, Stillwater, OK 74078-3072, USA<br />
1<br />
Phone: ++49 (0)9131 85 27603, 1 Fax: ++49 (0)9131 85 27293, *Email: jvz@optik.uni-erlangen.de<br />
We propose to employ photons emitted from single trapped ions to image a physical<br />
object of sub-wavelength size with 100% contrast by making use of joint detection<br />
probabilities.<br />
In quantum imaging, so far sub-classical spatial resolution has been achieved with 100 % contrast using<br />
entangled photons in combination with multi-photon absorbers [1,2]. In addition, it has been shown that<br />
using thermal light together with single photon detection enables to obtain sub-classical resolution, too,<br />
however with a contrast reduced to less than 50% [3]. Recently, we proposed a scheme achieving a spatial<br />
resolution of λ/N with 100 % contrast involving initially uncorrelated and incoherent photons<br />
spontaneously emitted from N equidistant single photon sources, e.g. trapped ions, and subsequently<br />
detected by N detectors in the far field [4]. For certain detector positions r2,…, rN, it was shown that the<br />
Nth order correlation function as a function of r1 takes the form 1 + cos N δ(r1) resulting in a fringe<br />
spacing given by λ/N. With δ(r) = k d sinθ(r) being the optical phase difference of photons emitted from<br />
adjacent sources involving the source distance d, the scheme, however, is limited to provide information<br />
only about the spatial distribution of the source itself.<br />
<strong>Here</strong> we propose to image a distinct physical object, e.g., an aperture, with sub-wavelength resolution<br />
and a contrast of 100% using the N single photon emitters as a light source in an ordinary far-field<br />
imaging scheme. An equal number of detectors as emitters - positioned in the far-field of the object -<br />
perform correlation measurements of the emitted photons that pass by the object (see fig. 1). We show<br />
that it is possible by exploiting quantum interferences between the different quantum paths of the<br />
photons to image and resolve the object with a resolution of λ/N.<br />
In case of a single aperture (of height a) and two 2-level ions used in a pulsed regime as single photon<br />
sources, the setup is shown below (see fig. 1). In a successful measurement cycle, the two ions at R1 and<br />
R2 each emit a single photon which both pass by the aperture - positioned in the far-field of the ions - and<br />
are recorded by two detectors in the far-field of the aperture at r1 and r2. Using standard far-field<br />
approximations and limiting the calculation to the x-z-plane the joint two photon detection probability is<br />
given for|r2x| = r1x , R1x = 0 and R2x = πRz/(ka) by<br />
G(2)( r1x) ~ sin 2 (2 δ(r1x))<br />
This function oscillates twice as fast as the classical intensity diffraction pattern I(rx) ~ sin 2 (δ(rx)) obtained<br />
conventionally with as single detector when recording diffracted classical light in the far-field of the<br />
aperture (see e.g. [5]). According to Abbe’s criterion of resolution this implies that sufficient information<br />
is available to image and resolve the aperture even if of heigth a = λ/2 (see fig. 2). In particular, for r2x = r1x
and using a two-photon absorbing medium placed in the image plane it is possible to image an aperture<br />
of sub-wavelength size using an optical lens.<br />
R 1<br />
x<br />
y<br />
z<br />
r 1<br />
R 2<br />
r 0<br />
|e<br />
0<br />
b<br />
a<br />
r 2<br />
|g<br />
Figure 1: Far-field imaging scheme achieving sub-wavelength<br />
resolution: Two single photon emitters, e.g. two trapped 2-level<br />
ions, are used as a source to irradiate and image a physical object,<br />
here a rectangular aperture of height a. The measurement can be<br />
either performed in the Fourier plane or in the image plane using<br />
an optical lens.<br />
Figure 2: Classical intensity diffraction pattern vs. second order<br />
correlation signal for the system shown in fig. 1. According to<br />
Abbe’s criterion an object can be imaged and resolved if at<br />
least the first order diffraction maxima are visible in the<br />
Fourier plane. According to this criterion the minimum<br />
distance that can be imaged and resolved in a classical setup is<br />
of the order of the wavelength λ (see e.g. [6]). By contrast, the<br />
minimum distance resolvable with the setup shown in fig. 1 is<br />
of the order of λ/2.<br />
References<br />
[1] A. N. Boto et al., Phys. Rev. Lett. 85, 2733 (2000)<br />
[2] M. D'Angelo, M. V. Chekhova, Y. Shih, Phys. Rev. Lett. 87, 013602 (2001)<br />
[3] G. Scarcelli, A. Valencia, Y. Shih, Europhys. Lett. 68, 618 (2004)<br />
[4] C. Thiel, T. Bastin, J. Martin, E. Solano, J. von Zanthier, G. S. Agarwal, submitted for publication<br />
[5] M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1980), 6th ed.
Towards ion trap array architectures with 171Yb+ ions<br />
James J. McLoughlin, Altaf H. Nizamani, James D. Siverns, Robin C. Sterling,<br />
Merlin Bevan-Stevenson, Nicholas Davies, Jessica Grove-Smith, Marcus Hughes,<br />
Ben Johnson, Kieran Lee, Ben S. Pruess, Rajiv Ramasawmy, David N. Scrivener,<br />
Tim Short, and Winfried K. Hensinger<br />
Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, UK<br />
We present experimental progress towards trapping171Yb+. The experiments are directed towards<br />
scaling the ion trap quantum computer via advanced shuttling operations inside sophisticated ion trap<br />
arrays. Ytterbium is one of the most suitable elements for quantum information processing (QIP) because<br />
of its simple atomic structure and accessible transitions.<br />
A number of lasers have been built for the experiment. Ionisation will be achieved via two photonionisation<br />
using 399 nm photons. Following ionisation, cooling will be accomplished using the 369 nm<br />
2S1/2 (F=1) -2P1/2 (F=0) dipole transition. Atoms can also decay into a low lying D-state as well<br />
as a 2F7/2 state (via collisions). To complete the cooling cycle, 935nm and 638nm re-pumping beams<br />
are applied. Off-resonant transitions to undesired hyperfine levels will also occur and repumping occurs<br />
via sideband excitation, with sidebands being generated via high frequency electro optic modulators<br />
and laser diode current modulation. Most lasers are in-house built external cavity diode lasers with<br />
exception of 369nm which is a frequency doubled laser. In order to maintain cooling and re-pumping it<br />
is vital the lasers are frequency locked. The locking scheme we have implemented consists of a 780nm<br />
laser that is locked to a rubidium atomic reference vapour cell. All other lasers are locked to this laser<br />
via a transfer cavity lock. This consists of a scanning Fabry-Perot cavity where the fringe separation<br />
between different wavelengths is held constant via computer controlled feedback to the individual lasers.<br />
This effectively drift stabilizes our laser sources to the rubidium atomic reference. Labview is being<br />
employed to measure the separation of different lasers during the cavity scan and to calculate the ratio<br />
of their peak separations. The result of this will produce an error signal that indicates the drift of each<br />
laser, whilst being independent of any thermal drift of the cavity.<br />
We will also describe our design and studies of radio-frequency application for ion traps, in particular,<br />
how to build helical resonators with high Q-factors. We have experimentally studied how different<br />
design parameters affect the Q-factor.<br />
A versatile vacuum system has been designed to cater for a wide variety of ion trap chips. With<br />
over 100 electrical connects the system will be able to host large ion trap arrays, and multiple optical<br />
access ports and atomic ovens support both symmetric and asymmetric traps. The design is optimized<br />
for fast trap turn-around times.<br />
Figure 1: Versatile vacuum system for<br />
the operation of advanced ion trap chips.<br />
Red lines show optical access making this<br />
system suitable for both symmetric and<br />
asymmetric trap structures. The vacuum<br />
systems hosts a chip carrier with<br />
100 electrical interconnects.<br />
We present an overview of the whole ion trapping experiment, including the design of the first ion<br />
trap and the imaging system.<br />
We have also developed a method to efficiently simulate the electric fields of novel ion trap geometries<br />
using the Boundary element simulation method and we will present first results.
METROLOGY
The 88 Sr + OpticalFrequencyStandardattheNational<br />
ResearchCouncil<br />
PierreDubé,AlanA.Madej,andJohnE.Bernard<br />
InstituteforNationalMeasurementStandards,<br />
NationalResearchCouncil,Ottawa,ON,CanadaK1A0R6<br />
E-mail:pierre.dube@nrc-cnrc.gc.ca<br />
Analmostidealfrequencyreferencecanberealizedwithalaser-cooledsingleionconfinedinan<br />
rfquadrupoletrap[1]. AttheNationalResearchCouncilofCanadawehavedevelopedanoptical<br />
frequencystandardbasedonthe 88 Sr + ion.<br />
Inourpresentsystem,asingle 88 Sr + ionisconfinedinanrfPaultrapandiscooledwithdiodelaser<br />
radiationusingthe5s 2 S 1/2 −5p 2 P 1/2 transitionat422nm.Thefrequencyofthislaserisreferencedto<br />
asaturatedabsorptionlinein 85 Rbforaccuratedetuningfromthecoolingtransitionlinecenter[2].In<br />
addition,apolarization-scrambledlaserat1092nmisrequiredduringthecoolingperiodtoprevent<br />
decayoftheiontothemetastable 2 D 3/2 state.Thereferencefrequencyin 88 Sr + isthe0.4Hzwide<br />
5s 2 S 1/2 –4d 2 D 5/2 transitionat445THz(674nm).Itscenterfrequencyisprobedwithanultra-stable<br />
andnarrow674nmdiodelasersystem.Thestabilityoftheprobelaserisprovidedbyahighfinesse<br />
referenceresonator(F =160000)whichisentirelymadeofultra-lowexpansioncoefficientglass<br />
(ULE). Itishousedinavibrationisolatedvacuumchamberthatisstabilizedatthetemperatureof<br />
zerothermalexpansioncoefficientoftheULEforoptimalstability. Linewidthsof5Hzhavebeen<br />
observedontheS–Dclocktransition.<br />
Duringthepastfewyears,thedemonstratedaccuracyofopticalfrequencystandardshasimproved<br />
bymorethanoneorderofmagnitudefollowingthedevelopmentofthefemtosecondlaserfrequency<br />
comb.Thistechnologyhasgivenustheopportunitytomakeadetailedstudyofthefrequencyshifts<br />
asafunctionofthequantizationaxisdirectionthatledtoasimpletechniqueforthecancellationofthe<br />
electricquadrupoleshiftandofthetensorpartoftheStarkshift[3].Theelectricquadrupoleshifthas<br />
itsoriginintheinteractionbetweenthequadrupolemomentoftheclocktransitionandtheresidual<br />
electricfieldgradientcausedbypatchpotentialsonthetrapelectrodes;itisoneofthemostimportant<br />
systematicshiftslimitingtheaccuracyofseveralsingleionfrequencystandards.Thistechniquehas<br />
beenusedtomakethemostaccuratefrequencymeasurementwiththe 88 Sr + iontodate[4]. An<br />
overviewofourexperimentalsetupusedtorealizethe 88 Sr + opticalfrequencystandardandrecent<br />
resultswillbepresentedattheworkshop.<br />
References<br />
[1] H.G.Dehmelt,“Mono-ionoscillatoraspotentialultimatelaserfrequencystandard,”IEEETrans.Instrum.<br />
Meas.,vol.IM-31,pp.83–87,1982.<br />
[2] A.D.Shiner,A.A.Madej,P.Dubé,andJ.E.Bernard,“AbsoluteopticalfrequencymeasurementofsaturatedabsorptionlinesinRbnear422nm,”Appl.Phys.B,vol.89,pp.595–601,2007.<br />
[3] P.Dubé,A.A.Madej,J.E.Bernard,L.Marmet,J.-S.Boulanger,andS.Cundy,“Electricquadrupoleshift<br />
cancellationinsingle-ionopticalfrequencystandards,”Phys.Rev.Lett.,vol.95,p.033001,2005.<br />
[4] H.S.Margolis,G.P.Barwood,G.Huang,H.A.Klein,S.N.Lea,K.Szymaniec,andP.Gill,“Hertz-level<br />
measurementoftheopticalclockfrequencyinasingle 88 Sr + ion,”Science,vol.306,pp.1355–1358,2004.
Towards Direct Frequency Comb Spectroscopy using Quantum Logic<br />
Borge Hemmerling, Lukas An der Lan, Piet O. Schmidt<br />
Institut fur Experimentalphysik, Universitat Innsbruck, Austria<br />
A possible change of the ne-structure constant over cosmological time scales<br />
derived from quasar absorption lines is currently strongly debated. One of the<br />
diculties turns out to be the lack of precise laboratory data on transition lines<br />
of elements with a complex level structure such as Ti + and Fe + [1].<br />
We challenge this problem by developing a versatile experimental setup in<br />
which spectroscopy ions are sympathetically cooled by magnesium ions in a<br />
linear Paul trap. Using quantum logic techniques, initial state preparation and<br />
state detection of the spectroscopy ion can be very ecient. Owing to the<br />
complex level structure of these spectroscopy ions, repumping from unwanted<br />
states is required. We plan to implement this by applying an appropriately<br />
tailored optical frequency comb.<br />
We will present the latest status of our experimental setup and simulation<br />
results on the expected uorescence signal from a Ca + test candidate. We<br />
furthermore present schemes based on quantum logic techniques to interrogate<br />
single ions in order to further improve the accuracy of the spectroscopic data.<br />
[1] J. C. Berengut, V. A. Dzuba, V. V. Flambaum, M. V. Marchenko and J.<br />
K. Webb, arXiv:physics/0408017 (2006)<br />
1
H 2 + vibrational spectroscopy : theoretical results and experimental<br />
developments<br />
Jean-Philippe Karr, Vladimir I. Korobov*, Jofre Pedregosa, Franck Bielsa,<br />
Albane Douillet and Laurent Hilico<br />
<strong>Laboratoire</strong> <strong>Kastler</strong> <strong>Brossel</strong>, UEVE, UPMC, ENS, CNRS<br />
Université d’Evry Val d’Essonne, Département de Physique<br />
boulevard F. Mitterrand, 91025 Evry<br />
E-mail :jean-philippe.karr@univ-evry.fr<br />
*Joint Institute for Nuclear Research, 141980, Dubna, Russia<br />
We develop a project aiming at direct optical determination of the proton to electron mass ratio with a<br />
relative accuracy in the 10 -10 range. It relies on Doppler free two-photon spectroscopy of H 2 + ions. Indeed,<br />
H 2 + ro-vibrational levels mainly depend on the Rydberg constant (known with a 6.6 x 10 -12 relative accuracy)<br />
and on m p /m e (4.3 x 10 -10 ). It also relies on the accurate ab-initio calculation of H 2 + energy levels at the 10 -10<br />
level.<br />
Because H 2 + is a homonuclear molecular ion, all bound ro-vibrational levels are metastable and all onephoton<br />
transitions between them are prohibited. Nevertheless, ro-vibrational levels with v ≥ 1 can be<br />
photodissociated by 248 nm UV photons (v is the vibrational quantum number).<br />
Doppler-free two-photon transitions in the infra-red domain (9-10 µm) are allowed and can be observed<br />
using 2 IR +1 UV ’ resonance enhanced multi-photon dissociation (REMPD) as shown in Fig. 1.<br />
From the theoretical point of view, the poster presents H 2 + ro-vibrational structure, two-photon transitions<br />
intensities (in atomic units in Fig. 2) and recent progress in radiative and relativistic corrections and<br />
hyperfine structure calculations, with a present accuracy level of 3 x 10 -10 .<br />
The experimental set-up first aims at probing the (v=0,L=2)→(v=1,L=2) two-photon transition where L<br />
is the total orbital angular momentum. The infra-red laser source is a quantum cascade laser (QCL) phaselocked<br />
to a HCOOH stabilized CO 2 laser. We present the spectral features of the QCL source (53 mW<br />
optical power, kHz linewidth, GHz tunability) as well as the injection in a high finesse Fabry-Perot cavity,<br />
and discuss the expected two-photon transition yield.<br />
The hyperbolic ion trap and photodissociation detection process are presented in another poster.<br />
Fig 1:<br />
Fig 2 :<br />
References:<br />
• http://physics.nist.gov/cuu/index.html<br />
• L. Hilico, N. Billy, B. Grémaud, D. Delande, J. Phys. B 34, 491-507, (2001)<br />
• J.-Ph. Karr, S. Kilic, L. Hilico, J. Phys. B 38, 853-66 (2005)<br />
• V.I Korobov, L. Hilico, J-Ph. Karr, Phys. Rev. A 74, 040502(R)/1-4 (2006)<br />
• J.-Ph. Karr, F. Bielsa, T. Valenzuela Salazar, A. Douillet, L. Hilico, V. I. Korobov, Can. J. Phys 85, 497-507 (2007)<br />
• V.I. Korobov, Phys. Rev. A. 77, 022509 (2008).<br />
• J.-Ph. Karr, F. Bielsa, A. Douillet, J. Pedregosa, V.I. Korobov and L. Hilico, to be published in Phys. Rev. A.<br />
Vibrational spectroscopy of H 2 + : hyperfine structure of two-photon transitions.<br />
• J.-Ph. Karr, V.I. Korobov and L. Hilico, to be published in Phys. Rev. A. Vibrational spectroscopy of H 2 + : precise<br />
evaluation of the Zeeman effect
Two photon ro-vibrational spectroscopy of H 2+ : From Hyperbolic to Linear RF trap<br />
J. Pedregosa Gutierrez, F. Bielsa, J-P. Karr, A. Douillet and L. Hilico<br />
<strong>Laboratoire</strong> <strong>Kastler</strong> <strong>Brossel</strong>, UEVE, UPMC, ENS, CNRS<br />
Université d'Evry Val d'Essonne, Département de Physique<br />
boulevard F. Mitterrand, 91025 Evry<br />
e-mail: pedregosa@spectro.jussieu.fr<br />
Abstract<br />
Experiments to obtain precise and reliable values of fundamental constants sometimes reaches such<br />
a level of complexity that they are only realized a single time, by a single research group. In<br />
particular, this is the case for the current accepted value of the proton mass [1], m p and the electron<br />
mass [2], m e , from which the ratio m e /m p can be deduced with a 4.3×10 −10 relative accuracy. For this<br />
reason, we are developing an experiment which will provide an independent measurement of m e /m p<br />
by performing two-photon Doppler free ro-vibrational spectroscopy if H 2<br />
+<br />
ions[3]. This technique is<br />
expected to improve the relative accuracy to the 1×10 −10 level. In order to achieve this goal, tunable<br />
and stable laser sources[4, 5] and trapped ions are required. The present poster will concentrate in<br />
this second aspect of the set-up. In particular, the current status and performance of our hyperbolic<br />
trap will be presented as well as the design for an upgrade of the system, which includes the<br />
development of a linear Paul trap (LPT). Through ion dynamic simulations we have obtain obtain<br />
an estimation of the ion cloud distributions for the hyperbolic and linear traps. A scheme of ion<br />
extraction for the LPT perpendicular to the trap axis has been demonstrated to be highly efficient<br />
(~80%) using simulations.<br />
Figure 1: Linear trap and optical bench<br />
Ref.<br />
[1] Van Dyck et al., Phys. Rev. Lett, 75, 3598 (1995)<br />
[2] G. Werth et al., Phys. Rev. Lett. 85, 011603 (2002)<br />
[3] L. Hilico et al., J. Phys. B : At. Mol. Phys, 34, 1 (2001)<br />
[4] F. Bielsa et al., Opt. Lett., 32, 1641 (2007)<br />
[5] See as well the other poster of our group: “H 2<br />
+<br />
vibrational spectroscopy: theoretical results and experimental<br />
developpements”
Broadly tunable sub-mW CW Narrowband mid-IR Laser Source for<br />
Molecular Spectroscopy<br />
Sergey Vasilyev, Stephan Schiller, and Alexander Nevsky<br />
Institute for Experimental Physics, Universitätsstr 1, 40225 Düsseldorf, Germany<br />
Arnaud Grisard, David Faye, Eric Lallier<br />
Thales Research and Technology, RD 128, 91767 Palaiseau cedex, France<br />
Z. Zhang, A. J. Boyland, J. K. Sahu, M. Ibsen, W. A. Clarkson<br />
Optoelectronics Research Centre University of Southampton Highfield, Southampton,SO17 1BJ<br />
United Kingdom<br />
The successful development of methods for cooling and trapping molecules is expected to lead<br />
to a demand for appropriate continuous-wave laser sources allowing performing high-resolution<br />
spectroscopy and internal state manipulation. One example is the search for parity violation<br />
effects on the vibrational spectra of chiral molecules.<br />
One spectral range of interest, so far not yet satisfactorily available, is the IR range beyond 4.5<br />
µm. The objective of our research project is the development of a widely tunable (5 - 15 µm)<br />
narrowband mid-IR laser source based on a nonlinear down conversion of 1.5 - 2.0 µm laser<br />
radiation to mid-IR spectral region using difference frequency generation (DFG) and optical<br />
parametric generation (OPO) in a Orientation-Patterned Gallium Arsenide (OP-GaAs) crystal.<br />
The OP-GaAs crystal combines a high nonlinearity, wide transparency range, and high thermal<br />
conductivity with merits of a quasi-phase-matching technique. Recently a method was developed<br />
for fabrication of large-size OP-GaAs structures by a combination of molecular beam epitaxy<br />
and hydride vapor phase epitaxy.<br />
Tunable mid-IR source based on the DFG between a narrowband broadly tunable high power<br />
EDFA (10 W, 1540-1570 nm) and thulium (Tm) doped fiber laser MOPA (1 W, 1945 nm) has<br />
been developed. DFG output wavelength was tunable from 7.6 µm to 8.2 µm with pm precision<br />
by tuning of the EDFA wavelength and the nonlinear crystal temperature. Mid-IR output power<br />
of 0.5 mW has been measured. The measured characteristics of the OP-GaAs sample<br />
demonstrate a high quality of the material<br />
Spectroscopic capabilities of the mid-IR source were tested by measuring of CH 4 absorption<br />
spectra. Objectives of further work are the development of 5 - 15 µm tunable narrowband fiber<br />
laser pumped OP-GaAs OPO source. As one practical application outside the field of cold<br />
molecules we can envision a DFG or OPO based compact multi-gas spectrometer for analysis of<br />
polluting gases.
Design of a battery-based low noise voltage source<br />
Anke Wagner 1 , Klaus Blaum 1,2,3 , Wolfgang Quint 2 , Birgit Schabinger 1 , Sven Sturm 1<br />
1 Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany<br />
2<br />
GSI Darmstadt, 64291 Darmstadt, Germany<br />
3 Max-Planck-Institut für Kernphysik, D-69117 Heidelberg<br />
Bound-state quantum electrodynamical (BS-QED) calculations can be tested by highprecision<br />
measurements of the magnetic moment of the electron bound in highlycharged<br />
ions [1]. Therefore it is planned to measure the g-factor of 40,48 Ca 17+,19+ ions<br />
in a double Penning-trap [2,3]. To reach the precision aimed for (δg/g~10 -9 ), highly<br />
stable voltage sources are needed to set the electrode-voltages. In order to eliminate<br />
possible disturbance sources for these power supplies a very stable supply voltage is<br />
required, which has to be independent of the electricity network in order to avoid<br />
noise and ground loops. To this end, a battery-based voltage source was designed.<br />
A single car-battery (12V) is used to generate the required output voltages (±15V,<br />
±5V) and a maximum current per channel of 1.5A. The dc-voltage is converted into<br />
ac-voltage by a sine-generator, amplified by a power amplifier and a transformer,<br />
commutated by a bridge rectifier and, finally, flattened by a filter, a choke and voltage<br />
controller. The voltage controller was also self-build, as no commercially available<br />
controller was able to meet the requirements. It was aimed for a stability better than<br />
10 -3 over the load and a noise floor exceeding the -120dBV/√Hz of a standard<br />
precision voltage source. To control and monitor the voltages as well as the currents,<br />
a microcontroller, connected to a PC, is used.<br />
The noise floor of the voltage source was tested to -145dBV/√Hz for frequencies<br />
below 30kHz and -155dBV/√Hz for frequencies above 30kHz, respectively. The long<br />
term stability is 10 -5 or better. The obtained results and the present performance of<br />
the battery-based voltage source will be presented.<br />
[1] G. Werth et al., Int. J. Mass Spectrom. (2006)<br />
[2] M. Vogel et al., Nucl. Inst. Meth. B 253, 7 (2005)<br />
[3] B. Schabinger et al., Journal of Physics: Conf. Series 58 (2007) 121-124
Test of QED and CPT via g-factors<br />
S. Kreim 1 , J. Alonso 1,2 , K. Blaum 1,2 , H.-J. Kluge 2 , W. Quint 2 , B. Schabinger 2 , S. Stahl 3 , S.<br />
Ulmer 1 , J. Verdu 1 , M. Vogel 4 , J. Walz 1 , G. Werth 1<br />
1 Johannes Gutenberg University, Institut fuer Physik, 55099 Mainz, Germany<br />
2 GSI, 64291 Darmstadt, Germany<br />
3 Stahl-Electronics, 67582 Mettenheim, Germany<br />
4 Imperial College London, U.K.<br />
The g-factor of the bound electron serves as sensitive test for bound-state quantum<br />
electrodynamics (BS-QED) calculations. High precision experiments using single ions in a<br />
double-Penning trap have been carried out in the past on hydrogen-like C 5+ [1] and O 7+ [2].<br />
Based on the experience with these systems we plan similar experiments on hydrogenic ions<br />
with higher nuclear charge Z. At present we work on Ca 19+ [3]. Since the BS-QED effects<br />
scale approximately with Z 2 this should allow higher sensitivity.<br />
Using novel detection techniques for observing induced spin flip transitions on a single<br />
particle [4] we are setting up a Penning trap experiment to measure the g-factor of the proton<br />
with high precision [5]. A similar experiment is planned for the future on the anti-proton. A<br />
comparison of the g-factors of both particles will represent a test of the CPT invariance.<br />
References<br />
[1] H.Haeffner et al., Phys. Rev. Lett. 85, 5308 (2000)<br />
[2] J. Verdu et al., Phys .Rev. Lett. 92, 093002 (2004)<br />
[3] B. Schabinger et al., J. Phys.: Conf. Series 58, 121 (2007) (Proc. HCI 2006, Belfast )<br />
[4] S. Stahl et al., J. Phys. B 38, 297 (2005)<br />
[5] J. Verdú et al., AIP Conf. Proc. 796, 260 (2005) (Proc. LEAP-05)
A single Ca + ion for optical frequency metrology<br />
C. Zumsteg, C. Champenois, G. Hagel, M. Houssin, D. Guyomarc’h, F. Vedel, M. Knoop<br />
PIIM, Université de Provence-CNRS, Centre de Saint Jérôme, case C21,<br />
13397 Marseille cedex 20, France.<br />
Rf trapped earth-alkaline ions are versatile candidates for frequency metrology. Among<br />
the candidates for an optical frequency standard, a single Ca+ ion is extremely attractive.<br />
The electric quadrupole transition at 729 nm proposed as frequency reference (clock transition)<br />
has a natural linewidth below 200 mHz corresponding to a quality factor of 2.10 15 ; the<br />
wavelengths of the required lasers lie in the visible and near-infrared domain.<br />
The ion is stored in a miniature radiofrequency trap, allowing interrogation times<br />
beyond an hour, and giving access to the Lamb-Dicke regime. Probing of the clock transition<br />
in a single ion is carried out using the quantum jump statistics as a function of the clock<br />
laser frequency. The integration time needed to record an excitation spectrum may reach a<br />
couple of seconds. The probing laser must therefore have an outstanding frequency stability<br />
on this time scale with a line width at the hertz level.<br />
Our local oscillator is a lab-built titanium-sapphire laser pumped with 5 W of laser<br />
radiation at 532 nm (Coherent Verdi V5). The pre-stabilisation stage consists of a Pound-<br />
Drever-Hall (PDH) lock onto a 30-cm Invar cavity. The cavity, which has a finesse of about<br />
1000, is isolated from external perturbations with a vacuum chamber. Measurement by an<br />
auto-correlation technique yields a linewidth below a few kHz with a resolution limited by<br />
the length of our optical fibre (10 km).<br />
Absolute frequency stabilisation of the clock laser on a<br />
high-finesse (F =100000) ULE cavity of 150mm length<br />
is under construction. In order to improve the stability<br />
of the clock laser, we have chosen a tapered geometry<br />
vertically supported near its midplane [1](see figure).<br />
Elastic deformation of the cavity has been analysed using<br />
a finite elements method to optimize the supporting<br />
surface. Improving the stability of the cavity length requires<br />
also the reduction of thermal fluctuations. Passive<br />
and active isolation stages, composed respectively<br />
by three thermal shields and by an active temperature<br />
stabilisation on the vacuum chamber, are under construction.<br />
Recent advancement regarding the realisation<br />
of the cavity and the clock laser, will be presented.<br />
[1] Lisheng Chen, John L. Hall, Jun Ye, Tao Yang, Erjun<br />
Zang, and Tianchu Li. Vibration-induced elastic<br />
deformation of Fabry-Perot cavities. Phys. Rev A,<br />
74:053801, 2006.<br />
Vertical ULE cavity of 150mm length
Search for Time-Variation of the Electron-Proton Mass Ratio with MilliKelvin<br />
Trapped Molecular Ions<br />
Brian Odom,<br />
Kavli Institute for Cosmological Physics<br />
University of Chicago<br />
Abstract:<br />
Most extensions of the standard model predict that if the fundamental constants vary with<br />
time, the electron-proton mass ratio should change 30-40 times more rapidly than the fine<br />
structure constant. However, in current model-independent laboratory searches, sensitivity to<br />
time-dependence of the electron-proton mass ratio lags behind that of the fine structure<br />
constant by two orders of magnitude. I present a proposal to improve sensitvity to timevariation<br />
of the electron-proton mass ratio using spectroscopy on milliKelvin trapped<br />
molecular ions. Specifically, the molecular ions of interest have a long-lived electronic state<br />
nearly degenerate with a highly-excited vibrational level of the electronic ground state.
MOLECULES AND INTERACTIONS
Structural characterization of the protonated,<br />
phosphorylated dipeptide [Gly-pTyrH] + in the gas phase<br />
Catarina F. Correia a , Undine Erlekam b , Philippe Maître b and Gilles<br />
Ohanessian a<br />
a <strong>Laboratoire</strong> des Mécanismes Réactionels, Département de Chimie, Ecole<br />
Polytechnique, CNRS, 91128, Palaiseau Cedex, France<br />
b <strong>Laboratoire</strong> de Chimie Physique, Université Paris Sud 11, CNRS, 91405<br />
Orsay Cedex, France<br />
Phosphorylation of alcoholic side chains is one of the most frequent posttranslational<br />
modifications (PTM) of proteins. It is known that the functionality<br />
of a protein changes with the degree of phosphorylation, which can<br />
most probably be referred to the conformational changes that are involved.<br />
In order to understand the reactivity/functionality of a phosphorylated protein,<br />
it is therefore imperative to explore its structural properties and to<br />
locate the phosphorylated side chain(s). Infrared Multi Photon Dissociation<br />
(IRMPD) spectroscopy, in combination with density functional theory<br />
(DFT) calculations, has been proven to be a suitable tool to distinguish between<br />
phosphorylated and non-phosphorylated residues in the protonated<br />
amino acids serine, threonine and tyrosine [1]. The results on the isolated<br />
amino acids allow for a bottom-up approach to characterize small phosphorylated<br />
peptides in the gas phase.<br />
<strong>Here</strong>, we present a combined experimental (IRMPD) and theoretical (DFT)<br />
study of the protonated dipeptide [Gly-pTyrH] + which can serve as a model<br />
system to explore the impact of a phosphorylated side chain on the structure<br />
of a small peptide. IRMPD spectroscopy is performed using tunable IR<br />
light from a free electron laser (FEL) and a Fourier transform ion cyclotron<br />
resonance (FT-ICR) mass spectrometer. The characteristic phosphate vibrations<br />
can be found in the energy range between 1000 and 1400 cm −1 .<br />
Interestingly, the spectrum of [Gly-pTyrH] + in this energy range differs significantly<br />
from that of the protonated amino acid [pTyrH] + . Comparison to<br />
calculated spectra shows that the experimental spectrum results from two<br />
different conformers.<br />
Currently the secondary structure of peptides is probed using the amide<br />
I and II bands. The spectral range above 1000 cm −1 is, however, often<br />
congested by other vibrational modes and combination bands. For an unambiguous<br />
structural assignment it is therefore desirable to find structural<br />
probes at lower energies. A setup is presented that allows one to trap and<br />
vibrationally cool molecular ions, to form weakly bound complexes and to<br />
investigate their vibrational modes below 1000 cm −1 .<br />
[1] C. F. Correia, P. O. Balaj, D. Scuderi, P. Maître, G. Ohanessian, J. Am. Chem. Soc.<br />
130, 3359 (2008).
A tandem mass spectrometer for photodissociation spectroscopy of cold<br />
biomolecular ions in the gas phase<br />
U. J. Lorenz, A. Svendsen, O. V. Boyarkin and T. R. Rizzo<br />
Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland<br />
Within recent years, spectroscopic studies of biomolecular ions in the gas phase have attracted<br />
increased interest since they allow for the systematic investigation of the intrinsic properties of<br />
biomolecules as well as their interactions with the solvent. They can thus be used to test quantum<br />
chemical calculations and to establish an understanding of biological systems at a molecular<br />
level. Ultraviolet (UV) and infrared (IR) spectroscopy have successfully been applied to this task,<br />
yet face the problem that with larger systems spectral congestion limits the amount of information<br />
that can be extracted.<br />
Our group has recently addressed this issue in studies on protonated aminoacids. The<br />
experimental setup comprises a tandem quadrupole mass spectrometer featuring a liquid helium<br />
cooled 22-pole ion trap in which the ions are cooled to 10 K. Spectral congestion due to thermal<br />
broadening can thus be considerably reduced [1]. Furthermore, by employing an IR/UV double<br />
resonance scheme conformation specific spectra can be obtained. Thus, congestion due to<br />
conformational heterogeneity can be eliminated.<br />
<strong>Here</strong> we present a second generation apparatus, schematically depicted below, which is currently<br />
under construction in our lab. The principle of operation will be as follows: Ions are produced by<br />
nano electrospray and enter into the vacuum region via a heated capillary. A Smith-type ion<br />
funnel [2] is used to transfer the ions efficiently to a hexapole ion trap from where ion packets are<br />
released periodically. After mass selection in a quadrupole mass filter they pass an octopole ion<br />
guide and are trapped in the 4 K cold 22-pole ion trap where they are cooled in collisions with<br />
helium. Subsequently, the ions are irradiated with a UV (IR) laser and released from the trap.<br />
Parent and fragment ions are then analyzed by means of a second quadrupole mass filter.<br />
A FAIMS stage (field asymmetric waveform ion mobility spectrometry) can be inserted between<br />
the needle and the transfer capillary which will allow for enhanced conformer selection [3].<br />
Furthermore, an orthogonal time of flight (TOF) mass spectrometer will be added after the 22-<br />
pole ion trap which will enable us to obtain the entire mass spectrum of the ion packet in a single<br />
machine cycle. We will explore possibilities to compress the ion packet that leaves the cold trap<br />
in the extraction region of the TOF MS in order to increase sensitivity.<br />
[1] O. V. Boyarkin, S. R. Mercier, A. Kamariotis, and T. R. Rizzo, J. Am. Chem. Soc. 2006, 128,<br />
2816.<br />
[2] J. S. Page, K. Tang, and R. D. Smith, Int. J. of Mass Spect. 2007, 265, 244.<br />
[3] R. W. Purves, R. Guevremont, S. Day, C. W. Pipich, and M. S. Matyjaszczyk, Rev. Sci.<br />
Instrum. 1998, 69, 4094.
Collinear laser spectroscopy with cooled and trapped radioisotopes at ISOLDE<br />
E. Mané 1 , J. Billowes 1 , K. Blaum 2 , P. Campbell 1 , B. Cheal 1 , D. Forest 3 , K. Flanagan 4 , G. Neyens 4 , R. Neugart 5 , G.<br />
Tungate 3 , P. Vingerhoets 4 , D. Yordanov 5 and The ISOLDE Collaboration 6<br />
1<br />
Schuster Laboratory, The University of Manchester, UK<br />
2<br />
GSI, Germany<br />
3<br />
School of Physics and Astronomy, The University of Birmingham, UK<br />
4<br />
IKS, KU Leuven, Belgium<br />
5<br />
University of Mainz, Germany<br />
6<br />
CERN, Switzerland<br />
Collinear laser spectroscopy is a fast, Dopplerfree technique for determining nuclear<br />
observables such as magnetic dipole moments, electric quadrupole moments, spins and changes in<br />
the meansquare charge radii. These information are extracted from the fluorescence detection of<br />
resonant photons along the hyperfine spectra of atomic transitions.<br />
The European Organization for Nuclear Research, CERN, hosts the world's premier isotope<br />
separator online facility, ISOLDE. This facility has gone through several upgrades, one of which is<br />
the recent installation of a gasfilled linear Paul trap after the high resolution separator sector. As<br />
well as providing beams with reduced transverse emittance and energy spread, this device is also<br />
able to accumulate the ions and release the sample in bunches with a definite time structure. This<br />
upgrade allowed collinear laser spectroscopy to be performed on cooled and bunched ions at<br />
ISOLDE for the first time.<br />
As an example, radioactive potassium and stable rubidium beams were delivered for study with a<br />
collinear laser spectroscopy setup. The cooling effect caused a 10fold reduction of the beam<br />
emittance with a longitudinal energy spread of less than 1eV for beams extracted at 30keV. The ion<br />
beam and laser were focussed and overlapped through a 1mm alignment aperture. The narrow ion<br />
beam required considerably less laser power, which reduced the background due to scattered light.<br />
By tuning the beam cooler to accumulate and release the ions in bunches of 10μs, and setting the<br />
detection system to record events during this time window, the signaltonoise ratio was reduced by<br />
a factor of 10 4 .<br />
This improvent has opened new prospects for optical measurements of radioisotopes located further<br />
from stability than has previously been possible at ISOLDE using high resolution collinear<br />
techniques.
Towards sympathetic cooling of charged proteins<br />
David Offenberg, Chaobo Zhang, Bernhard Roth, and Stephan Schiller<br />
Institut für Experimentalphysik, Heinrich-Heine-Universität Düsseldorf, Germany<br />
In our ion trap apparatus we can reliably produce ensembles of translationally cold<br />
polyatomic molecular ions, e. g. for high-resolution spectroscopic studies, interactions with<br />
radiation or neutral gases, or various other applications. The molecular ions are transferred to<br />
the gas phase using an electro-spray ionization source (ESI). Via an octopole ion guide the<br />
ions are guided to a linear radio frequency trap where they are sympathetically cooled by their<br />
mutual interaction with laser-cooled 138 Ba + ions. So far, singly-protonated AlexaFluor350<br />
ions (mass 411 amu) have been sympathetically cooled to less than 140 mK [1] and singlyprotonated<br />
glycyrrhetinic acid ions (mass 471 amu) even further to less than 80 mK. Our<br />
observations are well described by molecular dynamics simulations, which are used to<br />
determine the number of ions, their spatial distribution, and translational temperatures [2].<br />
Recently we could demonstrate the full potential of our apparatus by cooling highly charged<br />
proteins. First evaluations show, that in one example an ensemble of 160 laser-cooled 138 Ba +<br />
ions cooled 50 seventeenfold protonated cytochrome c ions (mass ~ 12400 amu) to less than<br />
1 K. To our knowledge this is by far the heaviest molecular ion sympathetically cooled up to<br />
now.<br />
[1]<br />
A. Ostendorf, C. B. Zhang, M. A. Wilson, D. Offenberg, B. Roth, and S. Schiller,<br />
Sympathetic Cooling of Complex Molecular Ions to Millikelvin Temperatures, Phys. Rev.<br />
Lett. 97, 243005 (2006) + Erratum, Phys. Rev. Lett. 100, 019904 (2008)<br />
[2]<br />
C. B. Zhang, D. Offenberg, B. Roth, M. A. Wilson, and S. Schiller, Molecular-dynamics<br />
simulations of cold single-species and multispecies ion ensembles in a linear Paul trap,<br />
Phys. Rev. A 76, 012719 (2007)
Cold Chemistry with Cold Ions<br />
Stefan Willitsch 1,2 , Martin T. Bell 2 , Alexander D. Gingell 2 , James M. Oldham 2 and<br />
Timothy P. Softley 2<br />
1 Department of Chemistry, University College London, London WC1H 0AJ, UK<br />
2 Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK<br />
The recent development of a range of techniques for producing “cold” molecules at<br />
very low translational temperatures T≤1 K in the gas phase has provided the<br />
opportunity for studying collisional processes in a new physical regime. A new<br />
experimental method to study reactive collisions between ions and neutral molecules<br />
at very low temperatures will be presented which allows for tunable collision energies<br />
and a variety of chemically diverse reaction partners 1 . Our technique relies on the<br />
combination of a quadrupole-guide velocity selector for the generation of cold neutral<br />
molecules with a facility to produce strongly ordered samples of laser-cooled ions in<br />
an ion trap usually referred to as Coulomb crystals. Because of the strong localization<br />
of the ions chemical reactions can be studied with single-particle sensitivity. Our new<br />
technique represents a general approach to study reactive collisions between ions and<br />
polar neutral molecules over a wide temperature range down to the cold regime and is<br />
particularly suited to investigate chemical reactions of astrophysical relevance at the<br />
low temperatures prevalent in the interstellar medium. We will report results on a<br />
proof-of-principle experiment on the chemical reaction between translationally cold<br />
CH 3 F molecules and laser-cooled Ca + ions to form CaF + and CH 3 which was studied<br />
in a collision energy range corresponding to 1-10 K. The characteristics of our coldmolecule<br />
sources and the performance of the new technique as well as perspectives<br />
for further developments will be discussed.<br />
1 S. Willitsch, M.T. Bell, A. D. Gingell, S. R. Procter and T. P. Softley, Phys. Rev. Lett. 100 (2008), 043203
Isotope selective trapping with linear Paul traps<br />
Shuichi Hasegawa<br />
School of Engineering, The University of Tokyo, Japan<br />
hasegawa@q.t.u-tokyo.ac.jp<br />
Linear Paul traps have good mass selectivity and can confine ions in a fixed<br />
space. Recent progress in quantum electronics, especially laser cooling<br />
techniques, led atoms and ions to low temperatures. Laser cooling of trapped<br />
ions allows the non-destructive observation of single ions through their laser<br />
induced fluorescence (LIF). The laser cooling also reduces the Doppler<br />
broadened linewidth, which enables one to resolve the isotope shifts of the ions.<br />
Therefore, we have proposed the application of the ion trapping and laser<br />
cooling techniques to the measurement of isotope ratios and trace isotope<br />
analysis [1]. In order to maximize the sensitivity, one needs to efficiently trap the<br />
isotope of interest. In this report, we show isotope selectivity of trapped ions with<br />
a linear Paul trap and observation of their LIFs using the laser cooling technique.<br />
Calcium ions are generated by pulsed Nd:YAG laser ablation. Slow ions can be<br />
trapped in the linear Paul trap. This method generates ions easily and a large<br />
number of ions can be loaded [2]. After cooling the trapped ions, we can observe<br />
the calcium isotopes. In order to purify the trapped isotopes, we scan the rf<br />
amplitude and static voltage applied to the electrodes, which correspond to q<br />
and a parameters of the Mathieu equations. Lighter mass isotopes ( 40, 42 Ca + )<br />
are repelled by the initial rf voltage conditions. By applying +8V to the electrode<br />
(U dc ), 48 Ca + are expelled from the trap and only 44 Ca + ions remain in it.<br />
We demonstrated the isotope selectivity of trapped ions by changing the<br />
voltages applied to the electrodes of the linear Paul trap. The results were<br />
confirmed by observing the laser induced fluorescence enhanced by the laser<br />
cooling method. This method can be utilized to efficiently accumulate a large<br />
number of rare isotopes and measure the isotope ratios.<br />
Acknowledgements: The author acknowledges the productive work of his colleagues,<br />
Y. Hashimoto, D. Nagamoto.<br />
References: [1] S. Hasegawa, et al. J. Nucl. Sci. Technol. 43, 300 (2006). [2] Y.<br />
Hashimoto, et al., Jpn. J. Appl. Phys. 45, 7108 (2006).
AN ION TRAP FOR LASER SPECTROSCOPY OF COLD HIGHLY-CHARGED IONS<br />
R.C. Thompson 1 , D.M. Segal 1 , S. Bharadia 1<br />
W. Nörtershäuser 2,3 , D.F.A. Winters 2 , M. Vogel 1,2 , Z. Andjelkovic 1,2<br />
and the SPECTRAP collaboration<br />
1 Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, UK<br />
2<br />
GSI mbH, Atomphysik, Planckstrasse 1, D-64291 Darmstadt, Germany<br />
3<br />
Uni Mainz, Institut für Kernchemie, Fritz-Strassmann-Weg 2, D-55099 Mainz, Germany<br />
We present an overview of SPECTRAP, an experiment under construction at GSI, which will<br />
perform high-precision laser spectroscopy measurements of the ground-state hyperfine splitting<br />
(HFS) of cold highly-charged ions (HCI), as a direct test of bound state QED at high fields. The<br />
experiment is situated in the new ion trap facility of HITRAP [1], which will be operational in late<br />
2008, and will be able to deliver approximately 10 5 cold (4K), bunched HCI to several Atomic<br />
Physics experiments [2].<br />
The ion trap, a cylindrical Penning trap, has been constructed and tested as a radio frequency trap.<br />
The experimental setup uses the RETRAP [3] cold-bore superconducting magnet. HCI from the<br />
HITRAP Cooler Trap will be captured in flight, resistively cooled and compressed using a rotating<br />
dipole field [4]. In resistive cooling, energy is lost from the ion motion via currents induced in an<br />
external cryogenically-cooled resistor within a resonant circuit. Cooling is required to reduce<br />
Doppler broadening of the (M1) transitions of interest and cloud compression is necessary to<br />
maximise the fluorescence from the ions. Laser spectroscopy will be performed with an on-axis<br />
laser beam that excites the hyperfine transition within the ion’s ground-state.<br />
We aim to measure the HFS with a relative precision of 10 −7 . By comparison of both H-like and<br />
Li-like ions of the same isotope, QED effects can be extracted, at the strongest electromagnetic<br />
fields available, on the level of a few percent [5].<br />
Currently at GSI, we are working on bringing the magnet online, which will be used with a local<br />
EBIT for early tests with heavy ions. At Imperial, due the availability of our own superconducting<br />
magnet, an identical ion trap will shortly be run in a Penning configuration with low charge light<br />
ions. This will allow us to test both the trap optics and the rotating wall drive.<br />
[1] T. Beier, et al,, Nucl. Instr. Meth. Phys. Res. B 235, 473 (2005)<br />
[2] "HITRAP: A facility at GSI for highly charged ions" H.-J. Kluge, et al, Advances in Quantum<br />
Chemistry 53 (2007) 83.<br />
[3] Lukas Gruber, et al, Phys. Scr. 71, 60-107 (2005)<br />
[4] D.F.A. Winters, A.M. Abdulla, J.R. Castrejón Pita, A. de Lange, D.M. Segal and<br />
R.C. Thompson, Nucl. Instr. Meth. Phys. Res. B 235, 201 (2005)<br />
[5] D.F.A. Winters, M. Vogel, D.M. Segal, R.C. Thompson and W. Nörtershäuser, Can. J. Phys<br />
85, 403-408 (2007)