Ph.D. Thesis - Physics

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Figure 7-20: Left: <strong>Ph</strong>otograph of Uraniborg 2. The electrodes are labeled with the voltage applied to each, as referenced in the text. Right: <strong>Ph</strong>otograph of Uraniborg 1 mounted in a CPGA. The width of the PCB trap is ∼ 1 cm. 2, indicating the labels given to each electrode, and second, the trap (Uraniborg 1 rather than 2) mounted in a CPGA chip carrier for installation into the cryostat. A copper braid (solder wick) was soldered to one of the dc electrodes, with the other end screwed into the 4 K baseplate, in an effort to heat sink the trap to 4 K. The strontium oven for trap loading was mounted on a 1 1/3 in. CF feedthrough which was mounted on the exterior octagon. The end of the oven was placed in a hole in one of the copper baffles. The hole was drilled at the approximate height of the trap. This particular oven was made of a thin stainless steel tube. Steel wires spot-welded to the feedthrough were spot-welded to strips of tantalum foil, which were then spot-welded to the steel tube, which was filled with strontium metal. The tantalum, which has a high electrical resistivity, serves to heat the oven with a lower level of current than would otherwise be needed. As it was, 2.0 A was sufficient for loading the trap, the lowest value of any oven the author has made. Imaging optics Optical breadboards were mounted at a proper level to address the ions, with lasers propa- gating roughly parallel to the plane of the trap electrodes. The 422 nm and 1092 nm lasers were set up on one side of the cryostat. Each passes through a series of collimating and focusing lenses before being coaligned on a dichroic mirror. The initial coalignment was done by eye. Their beam waists were minimized and the coalignment of the beams was fine-tuned using a ThorLabs beam profiler. On the other side of the cryostat, the 460 nm and 405 nm photoionization beams were brought to a focus at the trap center using a fast achromat from ThorLabs. 178
Figure 7-21: The two internal lenses mounted on the 40 K shield, above an ion trap. The top of the 40 K shield is mounted in the octagon, and may rotate by small amounts. The lenses are also mounted on a separate copper plate that can move freely, for centering the lenses. The lenses are mounted on a cage system, so that the focus to the trap can be adjusted. The detection and PI beams were made to counter-propagate across the trap. This setup has certain advantages and disadvantages. Counter-aligning was more practical given the geometry of the experimental setup and the space available on the optical table. Also, aligning was fairly easy. Normally, neutral strontium atoms would be observed using the 460 nm light. The beam of neutrals was centered on the trap, and then the height of the beam was adjusted to the height computed by CPO (about 1.3 mm). The detection lasers were then counter-aligned to this beam. Typically only small adjustments in the laser positions were then required to detect trapped ions. The disadvantage is mainly that back-reflections from the PI optics caused additional 422 nm scatter, which was reduced when the PI lasers were blocked after loading. Detection of ions was done on an Santa Barbara Instruments Group (SBIG) ST-3200ME CCD camera with a 422 nm interference filter in place (as in Ch. 5). The imaging optics are as follows. Inside the cryostat, two lenses were mounted on the 40 K shield, a 20 mm aspheric lens and a 150 mm achromat. The focusing light emerging from the cryostat was reflected off a silver mirror into another 150 mm achromat, which collimated the light and served as the focusing lens. A final 150 mm achromat focused the image onto the CCD. Fig. 7-21 shows the lens assembly, including the internal 20 mm asphere and 150 mm achromat, mounted above an ion trap. 179
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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
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
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: Figure 7-19: The plastic socket tha
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 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
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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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