Ph.D. Thesis - Physics

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5.3.2 Lasers and imaging Two lasers are required for Doppler cooling and detection of 88 Sr + ; these have wavelengths of 422 nm and 1092 nm. The 422 nm laser addresses the 5S 1/2 →5P 1/2 transition and provides the momentum transfer for Doppler cooling. Also, 422 nm photons are detected when imaging ions. The 1092 nm laser is a “repumper” that addresses the 4D 3/2 →5P 1/2 transition and prevents optical pumping to the metastable 4D 3/2 state. The level structure is depicted in Fig. 5-5. Both lasers are extended cavity diode lasers. The laser diode is mounted on a temperature- stabilized baseplate, and current (50 - 100 mA) is passed through it to produce laser radiation. An “extended cavity” is formed by using a grating to reflect the radiation back into the diode. This permits additional tuning of the laser frequency. After leaving the grating, the beam passes through an optical isolator, which is a device that prevents light from the far side of the isolator from being reflected back into the diode. This is essential for preventing any effects due to an unintended cavity being formed by some surface other than the grating; it also prevents overloading of the diode due to excessive feedback. Finally, mode-matching lenses are used to couple the beam into a single-mode fiber patch cord for delivery to the ion trap. Coupling efficiencies of ≈ 50 % are typical. The beams are outcoupled from the fibers onto fast achromatic lens pairs from Thorlabs for collimation. A telescope and a final focusing lens are used to produce the desired beam waists at the trap site. 1/e 2 waists of about 50 µm are normally used. Photoionization (PI) of neutral Sr atoms is done by a two-photon process. The first photon, at 461 nm, pumps the atoms from the 5s5s ground state into the 5s5p excited state, where the lowercase letters refer to the orbital angular momenta of each of the two valence electrons in the neutral atom. The second photon addresses a broad (≈ 3 nm) transition that pumps the atom from its excited state into an autoionizing state which lies above the dissociation energy. Thus, one electron is removed. This process was described in Ref. [BLW + 07]. The 460 nm radiation is produced by doubling the 920 nm output of a titanium sapphire (Ti-Saph) laser (Coherent model no. MBR-110), which is pumped by a 5 W Spectra Physics Millennia Pro solid-state laser. A Spectra-Physics WaveTrain doubler is used. The 405 nm laser is quite a bit simpler; we use the output of an ECDL with a readily-available 405 nm diode. Due to the width of the transition, no further frequency stabilization is needed. Level diagrams for the ionic and PI transitions are presented in Fig. 5-5. For the atomic ion trap experiments in Ch. 5-7, we used a CCD camera (part no. ST- 3200ME) from Santa Barbara Instrument Group. It features a 2184 × 1472 array of 6.8 µm × 6.8 µm pixels, and can be cooled to -10 ◦ C. The quantum efficiency at 422 nm is about 60 %. Light is imaged onto the CCD using a simple system of two 2 in. diameter achromatic doublets that are mounted vertically above the vacuum chamber. The lens closest to the 114
Figure 5-5: Left: Level diagram for the 88 Sr + ion, showing the Doppler cooling transition at 422 nm, the repumper at 1092 nm, and the sideband cooling and coherent operations laser at 674 nm. The spontaneous emission rate from the 5P 1/2 state is 20 MHz, with the ion decaying to 4D 3/2 ≈ 1/13 of the time. The lifetime of the 4D 5/2 state is ≈ 0.4 s. Right: Photoionization transitions for 88 Sr. A 460 nm photon pumps the atom from the 5s5s state to the excited 5s5p state, then a 405 nm photon takes the atom into an autoionizing level, resulting in the loss of a single electron. 115
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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
Page 64 and 65: and thus requires invocation of the
Page 66 and 67: Renormalization Group (DMRG), with
Page 68 and 69: 3.3 The bounds on precision In this
Page 70 and 71: Figure 3-1: A schematic of a generi
Page 72 and 73: Figure 3-3: The 11.7 T, 500 MHz sup
Page 74 and 75: . Figure 3-4: The above probe is a
Page 76 and 77: Figure 3-5: The CHFBr2 molecule. Al
Page 78 and 79: Figure 3-6: Frequency-domain spectr
Page 80 and 81: used to extract the answer is irrel
Page 83 and 84: Chapter 4 Theory and history of qua
Page 85 and 86: GND RF r ENDCAP 0 z 0 ENDCAP Ring T
Page 87 and 88: where Q is the charge of the trappe
Page 89 and 90: angular momentum along the quantiza
Page 91 and 92: emission from the excited state |
Page 93 and 94: selection rule ∆m = ±1 is applie
Page 95 and 96: Figure 4-3: Schematic diagram of sp
Page 97 and 98: to address an ion in state |↑〉
Page 99 and 100: the vibrational temperature is low.
Page 101 and 102: to the design of the trap itself. M
Page 103 and 104: to the quantum-mechanical ground st
Page 105 and 106: Chapter 5 Lattice ion traps for qua
Page 107 and 108: Figure 5-1: Schematic of the lattic
Page 109 and 110: Figure 5-3: Fit to Eq. 5.2 of the C
Page 111 and 112: Figure 5-4: The vacuum chamber for
Page 113: weeks. Low pressures depend on choo
Page 117 and 118: Figure 5-7: (a) Schematic of the cr
Page 119 and 120: (a) Lattice Trap Schematic TOP PLAT
Page 121 and 122: mix the microspheres evenly in the
Page 123 and 124: Using the expression for ωˆr deri
Page 125 and 126: 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
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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
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Figure 8-1: Schematic of the experi
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are in close agreement in the case
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8.2.3 Simulated coupling rates We n
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Johnson noise We begin our discussi
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should suffice. Note that the above
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Chapter 9 Measuring the interaction
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Figure 9-2: Left: Level diagram for
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Figure 9-5: Photograph of the micro
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A fit of the resulting curve return
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Figure 9-9: Linear fit of the ωˆy
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Figure 9-12: Heating rate as determ
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Chapter 10 Conclusions and outlook
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traps, linking ions using photons,
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Bibliography [ADM05] Paul M. Alsing
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[CGB + 94] J. I. Cirac, L. J. Garay
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[GME + 02] M. Greiner, O. Mandel, T
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[LCL + 07] D. R. Leibrandt, R. J. C
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[PC04a] D. Porras and J. I. Cirac.
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[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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