Ph.D. Thesis - Physics

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Figure 9-6: <strong>Ph</strong>otograph of the fork holding the wire, mounted above the trap in the vacuum chamber. The fork is machined from stainless steel, and ceramic spacers inserted into the arms of the fork provide the wire’s electrical isolation. The wire, due to its 25 µm width, may be difficult to see in the picture. A photograph of this setup is presented in Fig. 9-6. 9.2 Experimental methodology 9.2.1 Compensation and frequency measurements The measurement of secular frequencies is done as described before (Chs. 5-7). The measurement of compensation voltages was done in an interesting way that has not been described in this thesis before. The idea is to mix in the resonant voltage at the secular frequencies directly on the rf electrodes. If the ion is at the rf null, then it will not be excited by this field; otherwise, the excitation of the secular motion can be observed. Typically, a small voltage will be required at first to excite an uncompensated ion. As compensation improves, this voltage can be increased. 9.2.2 Heating rate measurements Heating rate measurements for higher levels of heating (many quanta/s) can be done using the method of Doppler recooling. This method was described theoretically in Ref. [WEL + 07] and then demonstrated experimentally in Ref. [ESL + 07]. The method consists of the fol- lowing steps: 1. Doppler cool a single ion to its steady-state fluorescence level. 2. Turn off the cooling laser for a period of time. 3. Switch on the cooling laser and record the ion’s fluorescence as a function of time. 206
A fit of the resulting curve returns the initial energy of the ion, provided that the laser detuning and intensity are well-known. The detuning and saturation parameter (related to the intensity) are plugged into the fit function, such that E0 is the only free parameter. The derivation of this formula is presented in the theoretical paper cited above. An experiment is repeated several times to get a good curve. Since heating is a stochastic process, the ion heats up by a different amount each time, and averaging is required to get a good value for the average heating rate. 9.3 Measurements In this section we present the data for one experimental run, bringing in the wire from a far distance (D > 4 mm) to D = 0.6 mm from the trapped ion. At each wire position, compensation was done and the vertical compensation voltage was recorded, the vertical and horizontal secular frequencies were recorded, and a heating rate measurement was performed. For all the measurements in this section, the trap drive frequency was Ω/(2π) = 14.74 MHz, with a drive voltage of Vrf ≈ 200 V. The center of the trap was set at ground, and the voltages on the other electrodes that yielded a compensated trap were between -10 and 10 V. Vertical compensation Two compensation voltages, called H and V , were varied as the wire is brought in. Each is a linear combination of the voltages on several of the dc electrodes, with H changing primarily the electric field in the ˆx direction, and V changing the field in the ˆy direction. Of the two, only V changes appreciably, since the wire is moving vertically down onto the ion, with a small offset (≈50 µm) for imaging the ion. The vertical wire positions are plotted in Fig. 9-7. We see that there is a monotonic but nonlinear dependence on the wire position. It is possible that the dc charge on the wire changes during the course of the experiment, either by discharging or by picking up stray charged particles from the (small) ambient pressure or photoelectrons induced by laser scatter. Secular frequencies We plot here in Fig. 9-8 the secular frequency measurements for the same set of wire positions as above. Only the horizontal (ωˆx) and vertical (ωˆy) frequencies are plotted. The secular frequencies fit well to a 1/D 2 dependence, as displayed in Fig. 9-9. The equations are ωˆy/ (2π) = 0.124/D 2 + 1.63 and ωˆx/ (2π) = 0.121/D 2 + 1.44, where ωˆy and ωˆx are the vertical and horizontal frequencies measured in 10 6 s −1 and d is the ion-wire distance measured in mm. 1.63 and 1.44 MHz are the values of ωˆy and ωˆx, respectively, when the wire is effectively at D = ∞, and is not influencing the trap at all. 207
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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
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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
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
Page 191 and 192: Figure 8-1: Schematic of the experi
Page 193 and 194: are in close agreement in the case
Page 195 and 196: 8.2.3 Simulated coupling rates We n
Page 197 and 198: Johnson noise We begin our discussi
Page 199 and 200: should suffice. Note that the above
Page 201 and 202: Chapter 9 Measuring the interaction
Page 203 and 204: Figure 9-2: Left: Level diagram for
Page 205: Figure 9-5: Photograph of the micro
Page 209 and 210: Figure 9-9: Linear fit of the ωˆy
Page 211 and 212: Figure 9-12: Heating rate as determ
Page 213 and 214: Chapter 10 Conclusions and outlook
Page 215 and 216: traps, linking ions using photons,
Page 217 and 218: Bibliography [ADM05] Paul M. Alsing
Page 219 and 220: [CGB + 94] J. I. Cirac, L. J. Garay
Page 221 and 222: [GME + 02] M. Greiner, O. Mandel, T
Page 223 and 224: [LCL + 07] D. R. Leibrandt, R. J. C
Page 225 and 226: [PC04a] D. Porras and J. I. Cirac.
Page 227 and 228: [TBZ05] L. Tian, R. Blatt, and P. Z
Page 229 and 230: Appendix A Matlab code for Ising mo
Page 231 and 232: err_result = mean(theerr) 231
Page 233 and 234: J = J0; Jt(1) = J; Bt(1) = B; for k
Page 235 and 236: A.3 Simulation with constant force
Page 237 and 238: Appendix B Mathematica code for ion
Page 239 and 240: 2 crystal_shape_6uraniborg.nb Out[6
Page 241 and 242: Appendix C How to trap ions in a cl
Page 243 and 244: Finally, we note that the chilled w
Page 245 and 246: C.4 Laser alignment and imaging As
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Ph.D. Thesis - Physics

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