Ph.D. Thesis - Physics

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Figure 5-6: Top-view schematic of the optics setup for the atomic ion lattice trap experiment. On the left, the 422 nm and 1092 nm beams are outcoupled from single-mode optical fibers and collimated using fast achromat pairs. The beams are focused to the desired waist at the trap center using telescopes, then coaligned on a dichroic mirror. On the right, the 460 nm and 405 nm photoionization beams arrive in the same single-mode optical fiber and are focused together using a single fast achromat pair, then directed to the trap. The CCD camera is mounted above the vacuum chamber. trap has a focal length of f1 = 150 mm, while the second has a focal length of f2 = 450 mm. This results in a theoretical magnification of 3 and an f-number of 1.7. A schematic of the optics for this experiment may be found in Fig. 5-6. 5.4 Experimental results for 88 Sr + trapping In this section, we present our observation of the stable confinement of 88 Sr + ions in a 6×6 lattice trap, and experimental verification of the model of the trap discussed in Sec. 5.2 by measuring the secular frequencies of the ions for one particular lattice site. The rf electrode is cut from a stainless steel mesh from Small Parts, Inc., Part No. PMX-045-A. It is mounted 1 mm above a grounded gold electrode on a ceramic pin grid array (CPGA) chip carrier (Fig. 5-7). An additional planar electrode (the “top plate”) is mounted 1 cm above the rf electrode, to help shield the ions from stray charges. Electrical connections to both the rf and ground electrodes were made using a UHV-compatible solder from Accu-Glass (part no. 110796). The vacuum chamber was baked out to a base pressure of 7×10 −10 torr. The trap is loaded with 88 Sr + by the photoionization process described above. Typical laser powers used are 10 µW of 422 and 50 µW of 1092, with 1/e 2 beam waists of 50 µm. For beams of this size, the increase in beam width over the size of the trap (Rayleigh range) is not a concern. Ions were observed as both clouds and crystals (Fig. 5-8). The cloud lifetime is quite short (O(10 s)), but a small crystal has been kept in the trap, illuminated with cooling light, for up to 15 minutes. This short lifetime is attributable to the vacuum pressure. 116
Figure 5-7: (a) Schematic of the cross-section of the trap assembly. The trap electrode is held above the CPGA center pad on top of two 1 mm thick glass slides. (b) <strong>Ph</strong>otograph of the trap mounted in the CPGA. Connections for rf and GND (the grounded bottom electrode) are shown, as are the optional control electrodes for the ˆx and ˆy directions. A typical voltage of V = 300 V at Ω/2π = 7.7 MHz was applied to the rf electrode. Nu- merical modeling of the resulting pseudopotential yields secular frequency values of ωˆr/2π = 300 kHz and ωˆz/2π = 600 kHz. In order to test the model, we measure both secular frequencies as functions of the applied rf voltage V . We also compute a trap depth of 0.3 eV, which is the energy required for an ion at the potential minimum to escape. Secular frequencies were measured for one site near the center of the lattice using the standard method of applying a low-amplitude (∼0.02 V) oscillating voltage to the top plate at the motional frequency of the ions. When each vibrational mode of the ions is stimulated, their heating causes measurable drops in the fluorescence intensity. This experiment was performed and compared to the model for several values of the drive voltage (Fig. 5-9). Agreement is very good; measured data points differ from the predicted values by at most 5%, an error that results mainly from the approximation of the trap electrodes as perfect two-dimensional conductors for simulation. Although other sites near the center were also loaded, secular frequency measurements are presented here for only one site of the lattice. To implement a quantum simulation using all 36 sites of such a lattice trap, the potentials at the edges of the trap would also need to be measured, which is outside the scope of this work. In summary, this experiment verifies the properties of lattice traps derived above. Ac- cordingly, it is with some confidence that we can evaluate this trap design by calculating the simulated coupling rates (Sec. 5.6). 117
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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
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: Figure 5-5: Left: Level diagram for
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
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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
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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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