Ph.D. Thesis - Physics

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5-15 Comparison of motional coupling rates in lattice and linear traps as a function of ion-ion distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5-16 Simulated J-coupling rates in lattice and linear traps. . . . . . . . . . . . . 126 5-17 Dependence of the trap depth on the trap scale for lattice traps at constant secular frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6-1 Schematic of a linear ion trap . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6-2 Trap electrode layout for the San Quentin trap. . . . . . . . . . . . . . . . . 133 6-3 Pseudopotentials for San Quentin. . . . . . . . . . . . . . . . . . . . . . . . 135 6-4 Trap depth and ion decompensation as a function of Vtop in San Quentin. . 136 6-5 Photograph of San Quentin. . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6-6 Photograph of San Quentin with top plate. . . . . . . . . . . . . . . . . . . 137 6-7 The experimental setup for measurements on San Quentin. . . . . . . . . . 138 6-8 Image of an ion cloud in San Quentin. . . . . . . . . . . . . . . . . . . . . . 139 6-9 Micromotion compensation measurements in San Quentin. . . . . . . . . . . 141 6-10 Photograph of the surface-electrode trap Bastille. . . . . . . . . . . . . . . . 142 6-11 Bastille mounted in a CPGA. . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6-12 Rf amplitude during ablation loading. . . . . . . . . . . . . . . . . . . . . . 144 6-13 Ablation experiment setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6-14 Ion signal as a function of the number of ablation pulses. . . . . . . . . . . 147 6-15 Trapped ion signal as a function of trap depth in Bastille. . . . . . . . . . . 148 6-16 Probability distribution for the number of ions loaded with a single ablation laser pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7-1 Schematic diagrams of Uraniborg 1 and 2 elliptical traps. . . . . . . . . . . 153 7-2 Calculated q parameters and trap depths as a function of rf voltage for the elliptical trap Uraniborg 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7-3 Calculated secular frequencies for Uraniborg 2 as a function of rf voltage. . 155 7-4 Elliptical trap secular frequencies as a function of trap size. . . . . . . . . . 156 7-5 Structure of small ion crystals in Uraniborg 2. . . . . . . . . . . . . . . . . . 157 7-6 Structure of larger ion crystals in Uraniborg 2. . . . . . . . . . . . . . . . . 158 7-7 Calculation of the transition from a 2-D to a 3-D crystal in Uraniborg 2. . . 159 7-8 Crystal structures for 120 ions in a symmetric (ωˆx = ωˆy) elliptical trap with a dc bias voltage along ˆz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 7-9 Calculation results for a simulated Ising model for two ion-qubits with a spatially and temporally constant force. . . . . . . . . . . . . . . . . . . . . 164 7-10 Calculation results for a simulated Ising model for two ion-qubits with a position-dependent force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 7-11 Calculation results for a simulated Ising model for two ion-qubits with a linear variation in time of the applied state-dependent force. . . . . . . . . . 166 16
7-12 Magnetic fields due to a “triple-Z” wire configuration. . . . . . . . . . . . . 168 7-13 J-coupling rates due to a “triple-Z” wire configuration as a function of trap size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 7-14 Magnetic fields due to a “concentric rings” wire configuration. . . . . . . . . 170 7-15 J-coupling rates as a function of trap size for the “concentric rings” wire configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7-16 Photograph of the expander for the closed-cycle cryostat. . . . . . . . . . . 172 7-17 Photograph of the exterior of the vacuum chamber surrounding the cryostat. 174 7-18 The 4 K baseplate of the closed-cycle cryostat. . . . . . . . . . . . . . . . . 175 7-19 The socket for the cryostat electrical connections. . . . . . . . . . . . . . . . 177 7-20 Photographs of Uraniborg 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7-21 Imaging optics mounted in the cryostat. . . . . . . . . . . . . . . . . . . . . 179 7-22 Secular frequency data for Uraniborg 2. . . . . . . . . . . . . . . . . . . . . 181 7-23 Calculated secular frequencies for Uraniborg 2. . . . . . . . . . . . . . . . . 181 7-24 Images of ion crystals in Uraniborg 2. . . . . . . . . . . . . . . . . . . . . . 182 8-1 Schematic of the experimental setup for ion-ion coupling over a wire. . . . . 191 8-2 Diagram of the model used in our calculations. . . . . . . . . . . . . . . . . 192 8-3 Equivalent circuit for two ions. . . . . . . . . . . . . . . . . . . . . . . . . . 196 9-1 Photograph of the vacuum chamber used for the ion-wire coupling experiment.202 9-2 Atomic level structure for the 40 Ca + ion and the Ca photoionization transitions.203 9-3 Photograph of the 397 nm laser. . . . . . . . . . . . . . . . . . . . . . . . . 204 9-4 Photograph of the 866 nm laser. . . . . . . . . . . . . . . . . . . . . . . . . 204 9-5 Photograph of the microfabricated trap used for ion-wire coupling experiments.205 9-6 Photograph of the fork holding the wire. . . . . . . . . . . . . . . . . . . . . 206 9-7 Measured dc vertical compensation values as a function of the height of the wire above the ion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 9-8 Horizontal (ωˆx) and vertical (ωˆy) secular frequencies as a function of the distance from the wire to the ion. . . . . . . . . . . . . . . . . . . . . . . . . 208 9-9 Fit of the secular frequencies as a function of ion-wire distance. . . . . . . . 209 9-10 Example Doppler recooling fit. Data points are an average of 200 measurements; error bars are statistical. . . . . . . . . . . . . . . . . . . . . . . . . . 210 9-11 Ion heating rate in eV/s as a function of ion-wire distance. . . . . . . . . . . 210 9-12 Ion heating rate in quanta/s as a function of ion-wire distance. . . . . . . . 211 17
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: List of Figures 2-1 The CNOT gate i
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
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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.
Page 227 and 228:
[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
Page 245 and 246:
C.4 Laser alignment and imaging As
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