Ph.D. Thesis - Physics

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1. Open the safety valve on the DMX-20. This is the only manually-controllable valve on that system. 2. Start a flow of helium gas through the DMX-20. Normally, you want to hear a faint flow of gas out the valve. 3. Reduce the pressure somewhat, then slowly close the valve so that the helium begins to make the bellows expand. After the bellows expands a good deal, or stops expanding, release the pressure using the manual valve. 4. Repeat this process at least five times. The idea is simply to thoroughly flush out the DMX-20. 5. Reduce the pressure from the gas cylinder slightly, then close off the valve. The steady-state pressure should leave the bellows somewhat expanded. As the system cools, one may observe the bellows contracting as the pressure of gas inside falls. If this happens, there is not quite sufficient pressure to the bellows. Increase, very slowly, the pressure until the bellows is slightly expanded. Also, aside from the helium used for flushing the system, there should be very little helium expended while running the cryostat. If the reading of the pressure inside the gas cylinder is visibly declining over a period of days, then either too much pressure is being supplied to the DMX-20, or there is a leak in the system. If a leak is suspected, make sure that all Swagelok connections are tight, and cannot be rotated. Leaks not only waste expensive UHP helium, but more seriously, can permit contaminants inside the DMX-20. This may permit water or nitrogen to freeze inside the bellows, creating a thermal short to the outside and destroying vibration isolation. If this occurs, the system must be warmed back up, and the bellows flushed again. C.2 Turning on the compressor Before turning on the compressor, the chilled water supply to and from the compressor must be opened (turn both handles at once). The compressor is turned on by insuring that the circuit breaker switch is in the “on” position (flipped up), and then flipping the green switch, which will light up when the compressor is on. Immediately, you should hear the motor begin to run, and also hear the pumping noise at about 2 Hz. The pressure gauge for the supply line will rise to > 300 psi, and should increase periodically, in time with the pumping action. If the motor begins running, but there is no periodic pumping (as evidenced by lack of sound and/ or pressure variation), then a blown fuse is the most likely culprit. On the front of the compressor, there are two easily accessible fuses. A fast-acting 250 V, 2 A fuse is required. 242
Finally, we note that the chilled water supply must be engaged whenever the cryostat is on, and must be switched off when the compressor is not running, to avoid water condensing on the hoses in places it shouldn’t. As a final caution, if the static pressure is below about 240 psi, then helium may need to be added. This should not need to happen very often, so if the pressure has fallen a good deal there may be a leak. We have, in the lab, a portable helium sniffer that can detect fairly large leaks. A mass spectrometer for vacuum systems may also be run in a sniffer mode, with higher sensitivity, if the proper attachment can be purchased or built. The author has experienced only one major helium leak, and it was located on the cold head itself (due to a manufacturing defect that has now been fixed). C.3 Pressure and temperature measurement The pressure inside the cryostat reaches UHV conditions in a matter of hours. However, it is not possible to directly measure the pressure near the 40 K or 4 K surfaces, since ionization gauges cannot run at cryogenic temperatures. Instead, we use the current reading on an ion pump attached to the vacuum chamber to measure the pressure outside the 4 K shield. We may reasonably assume that the pressure inside the radiation shield is significantly lower than that measured on the ion pump. For instance, if the ion pump reads 0.5 × 10 −9 torr, we may expect pressure in the 10 −11 torr range or better near the ion trap. The temperature is measured using two Lake Shore DT-670 diodes, across each of which a 10 µA current is passed. The voltage across the diode records the temperature, and the voltage-to-temperature conversion chart is reprinted below. There are two diodes, one of which is heat-sunk directly to the 4 K cold head, and the other of which is heat-sunk to the experimental 4 K baseplate. The former typically reaches a temperature of 5 K, while the latter normally reads 9-11 K. It is not known why the temperature is not lower, but modifying the heat sinking of wires or replacing the radiation shield with an all-copper piece may help, since copper is a better thermal conductor than stainless steel. 243
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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
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Figure 7-3: Calculated secular freq
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Figure 7-5: Left: Structure of 2-D
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Figure 7-7: Scaling of the order of
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involved. Because ions near the cen
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Results Before presenting the numer
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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
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
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: Appendix C How to trap ions in a cl
Page 245 and 246: C.4 Laser alignment and imaging As
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Ph.D. Thesis - Physics

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