Ph.D. Thesis - Physics

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7.6.1 Regular array of stationary qubits . . . . . . . . . . . . . . . . . . . 183 7.6.2 Sufficient controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 7.6.3 Decoherence rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 7.7 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . 185 III Toward ion-ion coupling over a wire 187 8 Motivation for and theory of ion-ion coupling over a wire 189 8.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.2 Theory of ion-ion coupling over a wire . . . . . . . . . . . . . . . . . . . . . 190 8.2.1 Electrostatic solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 8.2.2 Circuit model solution . . . . . . . . . . . . . . . . . . . . . . . . . . 193 8.2.3 Simulated coupling rates . . . . . . . . . . . . . . . . . . . . . . . . . 195 8.3 Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 8.3.1 Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.3.2 Electric field noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.4 Experimental questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 8.4.1 DC and RF paths from the wire to ground . . . . . . . . . . . . . . 198 8.4.2 Potentials on the wire due to the rf trapping fields . . . . . . . . . . 199 8.4.3 Heating rates vs. ion-wire distance . . . . . . . . . . . . . . . . . . . 199 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9 Measuring the interaction of a single ion with a wire 201 9.1 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 9.1.1 The 40 Ca + ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 9.1.2 The microfabricated trap . . . . . . . . . . . . . . . . . . . . . . . . 203 9.1.3 The wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 9.2 Experimental methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 9.2.1 Compensation and frequency measurements . . . . . . . . . . . . . . 206 9.2.2 Heating rate measurements . . . . . . . . . . . . . . . . . . . . . . . 206 9.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 10 Conclusions and outlook 213 A Matlab code for Ising model simulations 229 A.1 Simulation with constant force in space and time . . . . . . . . . . . . . . . 229 A.2 Simulation with a linear force gradient in space . . . . . . . . . . . . . . . . 232 A.3 Simulation with constant force in space and linear variation in time . . . . . 235 B Mathematica code for ion crystal structure 237 12
C How to trap ions in a closed-cycle cryostat 241 C.1 Preparing the cryostat for cooldown . . . . . . . . . . . . . . . . . . . . . . 241 C.2 Turning on the compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 C.3 Pressure and temperature measurement . . . . . . . . . . . . . . . . . . . . 243 C.4 Laser alignment and imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 245 C.5 What to do if you can’t trap ions . . . . . . . . . . . . . . . . . . . . . . . . 245 C.6 Shutdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 13
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 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
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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
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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
Page 245 and 246:
C.4 Laser alignment and imaging As
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