Ph.D. Thesis - Physics

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Electronics The electronics for this experiment were similar to those used in previous ones (Chs. 5 and 6). Briefly, dc voltages were supplied to four of the dc electrodes on the trap using an eight-channel voltage source that interfaces to the computer. The dc signals were filtered by standard R-C low-pass filters with a cutoff frequency of about 100 kHz. This was chosen to provide an rf short to ground for the dc electrodes at the drive frequency (3.5 MHz) while still allowing the lower-frequency voltages used for secular frequency measurement to pass through. An rf signal was produced by an Agilent 33250 function generator and sent directly to the helical resonator. To produce the proper voltages, no additional rf amplifier was required. The resonator was mounted to the table and connected to the chamber with an rf feedthrough. Grounding straps connected the rf input with the function generator, the cryostat hoses, and earth ground, and also provided the rf ground for the dc filters. 7.5.2 Secular frequency measurements Secular frequencies were measured by using a low-amplitude voltage applied to the electrode DC2. The amplitude required varied a great deal between the different motional frequencies. Prior to this, basic compensation of the trap was done by setting the dc voltages such that the ion cloud did not move when the rf amplitude was changed. There was actually a significant movement of the ion cloud (tens of microns) with a change in Vc of only 0.1 V; therefore, the vertical direction could be roughly compensated by setting Vc such that the cloud did not move out of the laser when the rf was changed. The final set of dc voltages were V1 = -3.90 V, V2 = 1.56 V, V3 = V4 = 0 V, and Vc = -2.62 V. Fig. 7-22 is a plot of one data set taken at a sequence of RF voltages with these dc voltages. The secular frequencies were measured by exciting the ions at their motional frequencies and observing drops in their fluorescence, as discussed in Sec. 5.4. The CPO-computed frequencies for this voltage set are plotted below, in Fig. 7-23. One sees that the agreement is not very good. Why is this? For one thing, note that the theoretical frequencies have changed a great deal from those with only rf confinement (cf. Fig. 7-3). Therefore, the dc voltages do not merely move the position of the ions; they change the curvature of the trap itself. A portion of the dc voltages here merely nulls stray fields that existed in the first place. Some portion, however, also contributes to altering the trap curvature. Another clue is provided by the fact that although ωˆx + ωˆy = ωˆz to fairly good agreement in the simulation, this relation does not hold for the experimental data, indicating that dc voltages have a contributing effect. Another possible source of error is that the rf voltage measured on the exterior of the cryostat does not necessarily equal the voltage on the trap. The degree to which it does depends greatly on the specific experimental setup. The wire extending from the feedthrough is quite long in order to reach the 4 K area and be properly heat-sunk on the 180
Figure 7-22: Measured secular frequencies as a function of rf voltage amplitude for the three motional modes of Uraniborg 2. ωˆx is blue, ωˆy is green, ωˆz is red, and ωˆz > ωˆx > ωˆy for all rf voltages. Errors on each frequency measurement are ±2 kHz. Figure 7-23: Calculated secular frequencies for the trap at 3.5 MHz and a series of rf amplitudes. The frequencies are blue, cyan, and green for ωˆx, ωˆy, and ωˆz, respectively, with ωˆz > ωˆx > ωˆy. 181
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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
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
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: Figure 7-21: The two internal lense
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 and 206: Figure 9-5: Photograph of the micro
Page 207 and 208: A fit of the resulting curve return
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
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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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