Ph.D. Thesis - Physics

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Figure 9-1: Photograph of the vacuum chamber used in Innsbruck for this ion-wire coupling experiment. The titanium sublimation pump is mounted on the left. Near the center, the ion pump, ion gauge, and main all-metal valve are mounted at an angle to the main axis of the chamber. The spherical octagon is on the right, with AR-coated CF35 (metric) viewports, roughly equivalent in diameter to 2 3/4 in. CF hardware. Sec. 9.2. Sec. 9.3 contains the experimental results, and in Sec. 9.4, we conclude and look to future experiments. 9.1 Experimental apparatus Much of the apparatus is similar to that used in Part II. The basic elements of a room temperature UHV system, and rf-driven Paul trap are the same as used at MIT on the strontium ion. The vacuum system is shown in Fig. 9-1. For the rest of the section, we focus on those elements that are substantially different from the MIT setup, including the ion species, the microfabricated gold surface-electrode trap, and the moveable wire. 9.1.1 The 40 Ca + ion The 40 Ca + ion has a level structure very similar to 88 Sr + . The structure is presented in Fig. 9-2. The laser wavelengths for 40 Ca + (that we used) are λDopp = 397 nm and λRep = 866 nm. The spontaneous decay rate of the P 1/2 level is 23 MHz with a branching ratio of 16. Ion production is accomplished by photoionization (PI) of a neutral calcium beam in a manner analogous to that used for strontium (Chs. 5 and 7). The requisite photons, 202
Figure 9-2: Left: Level diagram for the 40 Ca + ion, showing the Doppler cooling transition at 397 nm, the repumper at 866 nm, and the sideband cooling and coherent operations laser at 729 nm. The spontaneous emission rate from the 4P 1/2 state is 23 MHz, with the ion decaying to 3D 3/2 ≈ 1/16 of the time. The lifetime of the 3D 5/2 state is ≈ 1.2 s. Right: Photoionization transitions for 40 Ca. A 422 nm photon pumps the atom from the 4s4s state to the excited 4s4p state, then a 370 nm photon takes the atom into an autoionizing level, resulting in the loss of a single electron. at 422 and 370 nm, are generated from extended cavity diode lasers. A schematic of the two-photon PI process is also given in Fig. 9-2. The laser system was furnished by Toptica. The 397 nm Doppler cooling beam is produced by frequency-doubling a 794 nm laser diode, while the 866 nm radiation is produced from an extended cavity diode laser directly. Photographs of these lasers are presented in Fig. 9.1.1 and Fig. 9-4. The lasers are locked using the Pound-Drever-Hall (P-D-H) method to a four-hole ULE cavity under vacuum, with an approximate pressure of 10 −8 mbar. 1 The control electronics for current and temperature stabilization, as well as the P-D-H lock are furnished by Toptica. The frequencies are then monitored using a Toptica wavemeter. 9.1.2 The microfabricated trap The trap is manufactured using standard microfabrication techniques. The credit for the design and manufacture of the traps goes to Nikos Daniilidis, a post-doc in the Innsbruck group who collaborated on this project with Andreas Wallraff at ETH Zürich. The trap 1 In this chapter we shall use mbar rather than torr to describe vacuum pressures. Fortunately, 1 mbar = 0.75 torr, so that they are on the same order of magnitude. 203
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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
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
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: Chapter 9 Measuring the interaction
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 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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