Ph.D. Thesis - Physics

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Our experimental results are presented in Fig. 6-9. This composite figure illustrates several results. First, in (a), it shows that the cloud fluorescence intensity closely matches a Gaussian fit, allowing measurement of the cloud center to within ±0.5 µm. This translates into a precision of electric field measurement of about 10 V/m at zero field. The remainder of this figure shows our measurements of the ˆx and ˆy electric fields as a function of Vtop. This enables us to determine the required compensation voltages, Vtop = 1.0±0.1 V and V5 = 1.3±0.3 V. Either V4 or V5 could be used for compensating ˆx. It was convenient to use V5, since V4 was already used for the secular frequency measurement. The estimated residual displacement of a single ion at these voltages is 0.2 µm. The nonlinear dependence of Eˆy on Vtop is due to the anharmonicity of the trap along ˆy, unaccounted for in the above simple model. 6.3.3 Discussion Our measurements demonstrate that the compensation voltages for the trap do not agree well with the prediction of theory. At the theoretical compensation voltages V5 = 0 V and Vtop = -24.5 V, both Eˆx and Eˆy should be zero. We can determine the stray fields by measuring the actual values of Eˆx and Eˆy at these settings. At V5 = 0 V and with Eˆy = 0 (done by setting Vtop to 1 V), Eˆx was measured to be 30 V/m. Unfortunately, the trap was unstable at the ideal Vtop voltage. Instead of measuring Eˆy at this point, we extrapolate from Fig. 6-9, subfigure (c), that Eˆy ≈ 2000 V/m. This is in order-of-magnitude agreement with a parallel plate model, Eˆy = (Vexpt − Videal − V1)/d = 4200 V/m, where Vexpt is the measured compensation voltage (Vtop = 1.0 V), Videal is the ideal compensation value (Vtop = -24.5 V), and d is the distance between the top plate and the trap electrodes (d = 6.3 mm). Of course, these results depend on the agreement between our measured and predicted secular frequencies. They agree on a 5-10% level, with greater differences along ˆy, presumably due to the larger stray fields in that direction. These errors increase the uncertainty in our measurements a bit, but do not change the basic conclusions. The stray field along ˆx is comparable to those reported for 3-D ion traps [BMB + 98]. However, that along ˆy is on the order of 10 times larger. This suggests significant charging on either the dielectric on the ion trap, the top plate, or the observation window. This is clearly a problem when using PCB ion traps. Indeed, these stray fields all but prevented direct loading at UHV pressures, necessitating the use of the helium buffer gas. This is mainly because the stray field degrades the trap depth, although it also can cause excessive rf heating. This is due to the fact that, in the cloud state, driven micromotion couples to the secular motion. Before compensation, the UHV cloud lifetime was less than 10 s. Following compensation, ion cloud lifetimes of 10 minutes at 10 −9 torr were observed. This pressure was limited by residual buffer-gas pressure. As stated above, Rogers 4350B is a UHV-compatible material after bakeout. Subsequent PCB traps in vacuum have attained pressures in the 10 −11 torr range. 140
Figure 6-9: Measurement results showing compensation of micromotion in the trap at a helium buffer gas pressure of 1.0×10−5 torr. (a) Cloud intensity profile along the ˆy axis, fit to a Gaussian, for a representative value of the ˆy compensation voltage Vtop. (b) Linear fit of the cloud center position y0 versus 1/ω 2 ˆy,1 . Measurements in (a) and (b) permit measurement of the electric field Eˆy for a specific value of Vtop. (c) Plot of the ˆy electric field as a function of the Vtop voltage, showing that the stray field is minimized at Vtop = 1.0 V. (d) Plot of the ˆx electric field as a function of the middle electrode voltage V5, showing compensation at V5 = 1.3 V. 141
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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
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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
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: Figure 6-8: CCD image of a cloud of
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
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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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