Ph.D. Thesis - Physics

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COMPRESSED AIR 00000 11111 MICROSPHERE SOLUTION ELECTROSPRAY 4kV GND 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 0000 1111 CAMERA ~400V ~1−2 kHz RF TOP BOTTOM LASER Figure 5-11: Trapping apparatus. The lattice trap is inside a plastic chamber which can be pumped down to ≈ 1 torr. Macroions are loaded via the electrospray and the 4-rod trap, which extends through one side of the chamber over the surface of the lattice trap. 1.14 mm PUMP 1.14 mm Figure 5-12: Image from above of ions in the lattice. The dark holes are the holes in the rf electrode; the grounded plane is 1.4 mm beneath them. Single macroions appear as white dots that are levitated above the plane of the rf electrode and are illuminated by 532 nm laser radiation at 5 mW. White dots on the surface of the rf electrode are due to stray light scatter. The left image was taken at V = 300 V and Ω/2π = 1200 Hz and the right image was taken at V = 300 V and Ω/2π = 1960 Hz. In the left figure, in the top well, two ions are shown repelling each other in the same well. 120
mix the microspheres evenly in the solution, added 30 mL of methanol, and again sonicated for 10 minutes. Compressed air, at a pressure of between 3 and 5 Psi, forces the buffer solution first through a 0.45 µm filter and then to the electrospray system. Here a copper wire at a voltage of 4 kV is inserted in the tubing and ionizes the solution as it passes. The ionized solution travels through a thin electrospray tip directed at a perforated, grounded electrospray plate and a 4-rod Paul trap just behind the electrospray plate. The electrospray tips were made from capillary tubes, which are heated and stretched to produce narrow openings of 75-125 µm. As the solution enters the 4-rod trap, the methanol evaporates and the charged microspheres break into small clusters, the macroions. The 4-rod trap is driven at the drive parameters of the lattice trap and extends through the wall of a plastic chamber over the lattice trap. Inside the chamber, the 4-rod trap extends 0.75 cm over the lattice trap and the bottom rod of the 4-rod trap rests 1 mm above the ground plate. The lattice trap used for this work is shown in Fig 5-10. The trap is supported by standings inside the chamber, which can be closed on all sides to block air currents and can also be sealed and pumped down to ∼1 torr. Glass slides, which are coated with InTiO2 so that one side is conductive, act as the top plate. They allow a top view of the trap, and are supported approximately 15 mm above the rf plate. The ions are then confined approximately 0.25 mm above the plane of the rf plate. An image of the ions in the trap is given in Fig. 5-12. Typical initial loading parameters for macroions were Ω/2π = 1000 Hz and V = 250 V. We also applied a dc voltage of U = 0 − 10 V to the top plate to improve the trap depth. Before studying ion-ion repulsion, we estimate the Q/m of the macroions by measuring their secular frequencies (ωˆz). To do this, we apply a low-amplitude tickle to the top plate and observe the resonances directly on a video camera as ions rapidly oscillate back and forth. A measurement of ωˆz vs. Ω is shown in Fig. 5-13. Using Eq. 5.4, we fit these data to obtain a charge-to-mass ratio of 1.9 × 10 −9 ec/amu. We measured the Coulomb interaction of ions in neighboring lattice sites for six pairs of ions. In each pair, we measured the offset of each ion from the center of the well, as shown in Fig. 5-12. Note that while taking data on separation of two ions, we ascertained that wells adjacent to those containing the ions were all empty. The effect of a third ion in an adjacent well is significant. A simple model of the interaction of two ions across wells is given as follows. An ion is confined by a force −mω 2 ˆr x1, where x1 is the ion offset from the center of the well. Since generally x1 ≪ d, where d is the lattice spacing, the ion is approximately repelled by a force Q1Q2/4πǫ0sd 2 . Here s is a screening factor and Q1,2 are the charges of the first and second ion, respectively. The screening factor s < 3, where s = 3 for an ion sitting at a height 0.25 mm above an infinite conducting plane. 121
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An Investigation of Precision and S
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Acknowledgments What a long, strang
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should totally start a band. I also
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2.4 Conclusions and further questio
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7.6.1 Regular array of stationary q
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List of Figures 2-1 The CNOT gate i
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7-12 Magnetic fields due to a “tr
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Chapter 1 Introduction The growth o
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1.1 Quantum information The concept
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us whether the target system obeys
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Nevertheless, there are a number of
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Digital Analog Classical Quantum Sp
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electrodes [TKK + 99]. This heating
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Digital Analog Classical Quantum Sp
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2. Initialization to a simple fiduc
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qubits, and in Ref. [SGA + 05] in t
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the lattice architecture, we discov
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1.6 Contributions to this work In t
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5) Ref. [DLC + 09b] Wiring up trapp
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Chapter 2 Quantum simulation using
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µN the nuclear magneton, and B0 th
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⎡ ⎤ a 0 0 0 ⎢ ⎥ ⎢ ρ2 =
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The same effect as number 2 above i
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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
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: (a) Lattice Trap Schematic TOP PLAT
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
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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
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[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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Ph.D. Thesis - Physics

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