Ph.D. Thesis - Physics

More documents

Recommendations

Info

216
Bibliography [ADM05] Paul M. Alsing, Jonathan P. Dowling, and G. J. Milburn. Ion trap simulations of quantum fields in an expanding universe. Phys. Rev. Lett., 94, 220401, 2005. [AGDLHG05] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon. Simulated quantum computation of molecular energies. Science, 309, 1704, 2005. [AJL08] D. Aharonov, V. Jones, and Z. Landau. A polynomial quantum algorithm for approximating the jones polynomial. Algorithmica, 2008. [AL97] D. S. Abrams and S. Lloyd. Simulation of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett., 79, 2586, 1997. [AL99] Daniel S. Abrams and Seth Lloyd. Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett., 83(24), 5162–5165, 1999. [ALB + 07] M. Anderlini, P. J. Lee, B. J. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature, 448, 452, 2007. [ASA + 09] P. B. Antohi, D. Schuster, G. M. Akselrod, J. Labaziewicz, Y. Ge, Z. Lin, W. S. Bakr, and I. L. Chuang. Cryogenic ion trapping systems with surfaceelectrode traps. Rev. Sci. Instr., 80, 013103, 2009. [BB84] C. H. Bennett and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. pp. 175–179, IEEE International Conference of Computers, Systems and Signal Processing, Bangalore, India, 1984. [BBC + 93] C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A.Peres, and W. Wootters. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett., 70, 1895–1899, 1993. [BCC06] K. R. Brown, R. J. Clark, and I. L. Chuang. Limitations of quantum simulation examined by simulating a pairing Hamiltonian using nuclear magnetic resonance. Phys. Rev. Lett., 97, 050504, 2006. [BCJD99] G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch. Quantum logic gates in optical lattices. Phys. Rev. Lett., 82, 1060, 1999. [BCL + 07] K. R. Brown, R. J. Clark, J. Labaziewicz, P. Richerme, D. R. Leibrandt, and I. L. Chuang. Loading and characterization of a printed-circuit-board atomic ion trap. Phys. Rev. A, 75, 015401, 2007. 217
Page 1:
An Investigation of Precision and S
Page 5 and 6:
Acknowledgments What a long, strang
Page 7:
should totally start a band. I also
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
Page 57 and 58:
actions that occur between nuclei i
Page 59 and 60:
Figure 2-2: The 2,3-dibromothiophen
Page 61:
detail how this was done with a sim
Page 64 and 65:
and thus requires invocation of the
Page 66 and 67:
Renormalization Group (DMRG), with
Page 68 and 69:
3.3 The bounds on precision In this
Page 70 and 71:
Figure 3-1: A schematic of a generi
Page 72 and 73:
Figure 3-3: The 11.7 T, 500 MHz sup
Page 74 and 75:
. Figure 3-4: The above probe is a
Page 76 and 77:
Figure 3-5: The CHFBr2 molecule. Al
Page 78 and 79:
Figure 3-6: Frequency-domain spectr
Page 80 and 81:
used to extract the answer is irrel
Page 83 and 84:
Chapter 4 Theory and history of qua
Page 85 and 86:
GND RF r ENDCAP 0 z 0 ENDCAP Ring T
Page 87 and 88:
where Q is the charge of the trappe
Page 89 and 90:
angular momentum along the quantiza
Page 91 and 92:
emission from the excited state |
Page 93 and 94:
selection rule ∆m = ±1 is applie
Page 95 and 96:
Figure 4-3: Schematic diagram of sp
Page 97 and 98:
to address an ion in state |↑〉
Page 99 and 100:
the vibrational temperature is low.
Page 101 and 102:
to the design of the trap itself. M
Page 103 and 104:
to the quantum-mechanical ground st
Page 105 and 106:
Chapter 5 Lattice ion traps for qua
Page 107 and 108:
Figure 5-1: Schematic of the lattic
Page 109 and 110:
Figure 5-3: Fit to Eq. 5.2 of the C
Page 111 and 112:
Figure 5-4: The vacuum chamber for
Page 113 and 114:
weeks. Low pressures depend on choo
Page 115 and 116:
Figure 5-5: Left: Level diagram for
Page 117 and 118:
Figure 5-7: (a) Schematic of the cr
Page 119 and 120:
(a) Lattice Trap Schematic TOP PLAT
Page 121 and 122:
mix the microspheres evenly in the
Page 123 and 124:
Using the expression for ωˆr deri
Page 125 and 126:
Figure 5-15: Plot of the motional c
Page 127 and 128:
Figure 5-17: Dependence of the trap
Page 129 and 130:
Chapter 6 Surface-electrode PCB ion
Page 131 and 132:
Figure 6-1: Schematic of a linear i
Page 133 and 134:
Figure 6-2: Layout of the trap elec
Page 135 and 136:
Figure 6-3: Above are the cross sec
Page 137 and 138:
Figure 6-6: Photograph of the trap
Page 139 and 140:
Figure 6-8: CCD image of a cloud of
Page 141 and 142:
Figure 6-9: Measurement results sho
Page 143 and 144:
Figure 6-11: Bastille mounted in th
Page 145 and 146:
Figure 6-13: A diagram of the setup
Page 147 and 148:
Figure 6-14: A plot of the trapped
Page 149 and 150:
allows us to upper-bound the amount
Page 151 and 152:
Chapter 7 Quantum simulation in sur
Page 153 and 154:
Figure 7-1: Left: Uraniborg 1, as r
Page 155 and 156:
Figure 7-3: Calculated secular freq
Page 157 and 158:
Figure 7-5: Left: Structure of 2-D
Page 159 and 160:
Figure 7-7: Scaling of the order of
Page 161 and 162:
involved. Because ions near the cen
Page 163 and 164:
Results Before presenting the numer
Page 165 and 166: Figure 7-10: Calculation results fo
Page 167 and 168: 7.3 Magnetic gradient forces Now th
Page 169 and 170: Figure 7-13: Scaling of the J-coupl
Page 171 and 172: how are single-ion operations to be
Page 173 and 174: 250 psi, which increases to around
Page 175 and 176: Figure 7-18: At the center of this
Page 177 and 178: Figure 7-19: The plastic socket tha
Page 179 and 180: Figure 7-21: The two internal lense
Page 181 and 182: Figure 7-22: Measured secular frequ
Page 183 and 184: Along ˆy, the spacing is dˆy = 28
Page 185 and 186: of O2 to 2 × 10 −12 torr. Decohe
Page 187 and 188: Part III Toward ion-ion coupling ov
Page 189 and 190: Chapter 8 Motivation for and theory
Page 191 and 192: Figure 8-1: Schematic of the experi
Page 193 and 194: are in close agreement in the case
Page 195 and 196: 8.2.3 Simulated coupling rates We n
Page 197 and 198: Johnson noise We begin our discussi
Page 199 and 200: should suffice. Note that the above
Page 201 and 202: Chapter 9 Measuring the interaction
Page 203 and 204: Figure 9-2: Left: Level diagram for
Page 205 and 206: Figure 9-5: Photograph of the micro
Page 207 and 208: A fit of the resulting curve return
Page 209 and 210: Figure 9-9: Linear fit of the ωˆy
Page 211 and 212: Figure 9-12: Heating rate as determ
Page 213 and 214: Chapter 10 Conclusions and outlook
Page 215: traps, linking ions using photons,
Page 219 and 220: [CGB + 94] J. I. Cirac, L. J. Garay
Page 221 and 222: [GME + 02] M. Greiner, O. Mandel, T
Page 223 and 224: [LCL + 07] D. R. Leibrandt, R. J. C
Page 225 and 226: [PC04a] D. Porras and J. I. Cirac.
Page 227 and 228: [TBZ05] L. Tian, R. Blatt, and P. Z
Page 229 and 230: Appendix A Matlab code for Ising mo
Page 231 and 232: err_result = mean(theerr) 231
Page 233 and 234: J = J0; Jt(1) = J; Bt(1) = B; for k
Page 235 and 236: A.3 Simulation with constant force
Page 237 and 238: Appendix B Mathematica code for ion
Page 239 and 240: 2 crystal_shape_6uraniborg.nb Out[6
Page 241 and 242: Appendix C How to trap ions in a cl
Page 243 and 244: Finally, we note that the chilled w
Page 245 and 246: C.4 Laser alignment and imaging As
show all

Ph.D. Thesis - Physics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?