Ph.D. Thesis - Physics

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from the bottom of my heart, that I did not end up in the oven. I would also like to thank two collaborators on the lattice trap project, Yufei Ge and Tongyan Lin. Yufei, the undisputed master of trap fabrication at MIT, did a lot of fabrication and trap assembly for me, and Tongyan was a great collaborator throughout the arduous process of writing the lattice paper. I would also like to thank some folks at MIT who really helped us get started in the ion trap business, including Marko Cetina and Andrew Grier, who were building their first ion trap at about the same time we were; Dave Kielpinski, who helped fill in a lot of the gaps in our basic ion trap knowledge; and Prof. Vladan Vuletic, who imparted to us a small but sufficient fraction of his vast knowledge of lasers and AMO physics. Ich möchte auch meinen Kollegen, die ich in Innsbruck getroffen habe, herzlich danken. Es war ja eine besondere Gelegenheit, eine kurze Zeit mit euch zu arbeiten und zu wohnen. Hartmut - vielen Dank für deine Hilfe und Lehren, und auch für einige schöne kurze Reisen in die Berge um Innsbruck herum. Ich danke auch Rainer Blatt, der so nett war, mich in seinem Labor willkommen zu heissen. Ich habe viel über Ionenfallen von ihm und seiner Arbeitsgruppe gelernt. Meine Frau und ich werden uns auch immer an den schönen Abend bei Herrn und Frau Draxl und ihren köstlichen Schnaps erinnern. Ich danke auch Christian Roos, Volckmar Nebendahl, und Piet Schmidt für die guten Diskussionen über Physik, und Wolfgang Hänsel für die guten Diskussionen über Physik und Musik. Herzlichen Dank an Jan Benhelm und Gerhard Kirchmair für ihre Hilfe und Geduld mit den PI-Lasern. Ich habe viele neue Freunde in Innsbruck bekommen. Mit diesen Männern hatte ich, meistens ausserhalb des Labors, viel Spass. Ich danke Max “Captain Schnitzel” Harlander, Börge Hemmerling, und Lukas an der Lan, nicht nur für viele nette Abende, sondern auch für ihren Rat mit den Ionenfallen. Die Weisswurst-Kochgruppe wird immer ein Beispiel von Wie echte Männer Mittags essen sollen sein. I would like to apologize for my horrible German, and also to thank the non-German- speaking members of the Innsbruck group. My collaborators Tony Lee, Nikos Daniilidis, and Sankar Narayanan were a pleasure to work with. They each brought a new perspective into the lab. I’d like to thank Nikos for some great times outside the lab too, especially our September trip to a little party they were having up in Munich, and for being willing to go for a hike when we were working on a beautiful Saturday. Thanks are due to Tony for showing me the ropes in the CCT lab, for increasing my tolerance of piano music (which I do enjoy in moderate amounts), and for occasionally sharing an offensive joke. Rene Gerritsma was always available for good conversation over a slice of pizza and a Kaiser, and I owe Felicity Splatt thanks for a good deal of discussion about the trials and tribulations of microtraps. Coming now to the later years of my Ph.D., there are still more colleagues and friends to acknowledge. It was a pleasure to be joined in the lab by Shannon Wang, with whom I’ve had useful scientific and musical discussions. I appreciate the opportunities I’ve had to enjoy Shannon’s singing voice, from chamber concerts to my own wedding. Shannon - you 6
should totally start a band. I also owe much to Paul Antohi for his assistance with setting up the new cryostat. Kenan Diab, an undergraduate with whom I’ve worked recently, is a really smart guy, and it was an honor to work with him on something relatively practical, before he goes on to discover the Theory of Everything. Other colleagues with whom I’ve shared some good discussions and great times are, in no particular order: Liz George, Ruth Shewmon, Arghavan Safavi-Naini, Chris Pearson, Dave Schuster, Josh Folk, Terri Yu, and Peter Herskind. Thanks to all of you! In addition to the above individuals, there are some friends I’ve had in Boston without whom it would have been most challenging to hold on to my sanity. I’d like to thank Doug and Bory Eastman for a lot of great times and some unique experiences. I’d also like to thank Simon Myrgren, who was a pleasure to room with and to hang out with. It was a lot of fun to live with and enjoy some scientific, musical, and philosophical discussions with Andrew and Abigail Cross. I know someday my grandchildren will scarcely believe that I was at the world premier of “Tonya and Nancy: The Opera.” I’d also like to acknowledge my final roommate in Boston, Andy Klettke, and thank him for the good times we had. Finally, I’d like to thank two fellow Ohioans, who followed me out to Boston (cough), and were a great source of support all the while, Ryan and Stephanie Alvanos. When I think of all the busking, concerts, hanging out, camping trips, and sundry other activities that helped me to keep my cool during these six years, I am profoundly grateful. I wish you all the best until you follow me to Austin! This brings me to my family. I can’t thank my mother and father, Priscilla and James Clark, enough for their love and support over all these years. Without them, needless to say, I would not exist, much less have made it through graduate school. I’d like to thank Derek Clark for being a great brother, and Sarabeth Wilson for being a good girlfriend to him and friend to me. I appreciate all that Joanne Clark has done for me, as well. I also thank Mary and Paul Leidel for being great in-laws. It’s a bit unbelievable that this is really the end of the long, long period of long, long distance between me and my wife, Christina. Bumi - thank you so much for your patience, your love, and your support, from the moment I got into MIT and we had to part ways, through the moment I sprung that little surprise on you in New York, all the way to Erterreinpratz, our wedding, Ireland, and our house in Texas. It’s been a great journey already, even though we’re really still just at the beginning. You may tell the kids I’m on my way home. Finally, I’d like to thank my grandparents, Gertrude and Russell Clark, and Joan Day- ton, for all their support and love over the years. Sadly, one of my grandparents departed this world just before the completion of this work, but I believe he would have been as proud of me and as full of encouragement as he was during the rest of my life. This thesis is dedicated to the memory of Robert Jean Dayton. 7
Page 1: An Investigation of Precision and S
Page 5: Acknowledgments What a long, strang
Page 10 and 11: 2.4 Conclusions and further questio
Page 12 and 13: 7.6.1 Regular array of stationary q
Page 15 and 16: List of Figures 2-1 The CNOT gate i
Page 17: 7-12 Magnetic fields due to a “tr
Page 21 and 22: Chapter 1 Introduction The growth o
Page 23 and 24: 1.1 Quantum information The concept
Page 25 and 26: us whether the target system obeys
Page 27 and 28: Nevertheless, there are a number of
Page 29 and 30: Digital Analog Classical Quantum Sp
Page 31 and 32: electrodes [TKK + 99]. This heating
Page 33 and 34: Digital Analog Classical Quantum Sp
Page 35 and 36: 2. Initialization to a simple fiduc
Page 37 and 38: qubits, and in Ref. [SGA + 05] in t
Page 39 and 40: the lattice architecture, we discov
Page 41 and 42: 1.6 Contributions to this work In t
Page 43: 5) Ref. [DLC + 09b] Wiring up trapp
Page 47 and 48: Chapter 2 Quantum simulation using
Page 49 and 50: µN the nuclear magneton, and B0 th
Page 51 and 52: ⎡ ⎤ a 0 0 0 ⎢ ⎥ ⎢ ρ2 =
Page 53 and 54: The same effect as number 2 above i
Page 55 and 56: where V0 is the maximum signal stre
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actions that occur between nuclei i
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Figure 2-2: The 2,3-dibromothiophen
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detail how this was done with a sim
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and thus requires invocation of the
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Renormalization Group (DMRG), with
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3.3 The bounds on precision In this
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Figure 3-1: A schematic of a generi
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Figure 3-3: The 11.7 T, 500 MHz sup
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. Figure 3-4: The above probe is a
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Figure 3-5: The CHFBr2 molecule. Al
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Figure 3-6: Frequency-domain spectr
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used to extract the answer is irrel
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Chapter 4 Theory and history of qua
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GND RF r ENDCAP 0 z 0 ENDCAP Ring T
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where Q is the charge of the trappe
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angular momentum along the quantiza
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emission from the excited state |
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selection rule ∆m = ±1 is applie
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Figure 4-3: Schematic diagram of sp
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to address an ion in state |↑〉
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the vibrational temperature is low.
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to the design of the trap itself. M
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to the quantum-mechanical ground st
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Chapter 5 Lattice ion traps for qua
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Figure 5-1: Schematic of the lattic
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Figure 5-3: Fit to Eq. 5.2 of the C
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Figure 5-4: The vacuum chamber for
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weeks. Low pressures depend on choo
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Figure 5-5: Left: Level diagram for
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Figure 5-7: (a) Schematic of the cr
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(a) Lattice Trap Schematic TOP PLAT
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mix the microspheres evenly in the
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Using the expression for ωˆr deri
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Figure 5-15: Plot of the motional c
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Figure 5-17: Dependence of the trap
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Chapter 6 Surface-electrode PCB ion
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Figure 6-1: Schematic of a linear i
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Figure 6-2: Layout of the trap elec
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Figure 6-3: Above are the cross sec
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Figure 6-6: Photograph of the trap
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Figure 6-8: CCD image of a cloud of
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Figure 6-9: Measurement results sho
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Figure 6-11: Bastille mounted in th
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Figure 6-13: A diagram of the setup
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Figure 6-14: A plot of the trapped
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allows us to upper-bound the amount
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Chapter 7 Quantum simulation in sur
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Figure 7-1: Left: Uraniborg 1, as r
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Figure 7-3: Calculated secular freq
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Figure 7-5: Left: Structure of 2-D
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Figure 7-7: Scaling of the order of
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involved. Because ions near the cen
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Results Before presenting the numer
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Figure 7-10: Calculation results fo
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7.3 Magnetic gradient forces Now th
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Figure 7-13: Scaling of the J-coupl
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how are single-ion operations to be
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250 psi, which increases to around
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Figure 7-18: At the center of this
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Figure 7-19: The plastic socket tha
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Figure 7-21: The two internal lense
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Figure 7-22: Measured secular frequ
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Along ˆy, the spacing is dˆy = 28
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of O2 to 2 × 10 −12 torr. Decohe
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Part III Toward ion-ion coupling ov
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Chapter 8 Motivation for and theory
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Figure 8-1: Schematic of the experi
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are in close agreement in the case
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8.2.3 Simulated coupling rates We n
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Johnson noise We begin our discussi
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should suffice. Note that the above
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Chapter 9 Measuring the interaction
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Figure 9-2: Left: Level diagram for
Page 205 and 206:
Figure 9-5: Photograph of the micro
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A fit of the resulting curve return
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Figure 9-9: Linear fit of the ωˆy
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Figure 9-12: Heating rate as determ
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Chapter 10 Conclusions and outlook
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traps, linking ions using photons,
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Bibliography [ADM05] Paul M. Alsing
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[CGB + 94] J. I. Cirac, L. J. Garay
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[GME + 02] M. Greiner, O. Mandel, T
Page 223 and 224:
[LCL + 07] D. R. Leibrandt, R. J. C
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[PC04a] D. Porras and J. I. Cirac.
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[TBZ05] L. Tian, R. Blatt, and P. Z
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Appendix A Matlab code for Ising mo
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err_result = mean(theerr) 231
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J = J0; Jt(1) = J; Bt(1) = B; for k
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A.3 Simulation with constant force
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Appendix B Mathematica code for ion
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2 crystal_shape_6uraniborg.nb Out[6
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Appendix C How to trap ions in a cl
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Finally, we note that the chilled w
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C.4 Laser alignment and imaging As
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