Ph.D. Thesis - Physics

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[CBB + 05]. Surface-electrode traps are easier to fabricate than their 3-D counterparts, but have a lower trap depth. Because there exist methods that are capable of loading traps with depths on the order of 100 meV, which is considerably less than conventional macroscopic ion traps, we have chosen to exploit the simpler fabrication processes required for surface-electrode traps. Following Chiaverini’s proposal, a number of surface-electrode traps were demonstrated. The first such trap came from the Wineland group in a paper by S. Seidelin et al. [SCR + 06]. This trap was made of gold electrodes patterned on quartz. They demonstrated confirma- tion of the trapping potentials, ion crystallization, and a heating rate of 5000 quanta/s. This is the world record low for electric field noise in a room-temperature ion trap (scaled to ion-electrode distance and trap frequency). Heating rates as low as 5 quanta/s were subsequently demonstrated by Labaziewicz et al. in traps that were cryogenically cooled to 6 K [LGA + 08]. This work built on a previous study from the Monroe group that showed dramatic suppression of heating rates when trap electrodes were cooled to 150 K [DOS + 06]. Chronologically in between the Seidelin and Labaziewicz papers, our group pioneered the use of printed circuit boards (PCB’s) for ion trapping. The first publication along these lines came in 2006, when the Chuang group at M.I.T. (of which the author is a member) used PCB traps to confine charged macroscopic particles and demonstrate all the basic ion movement operations in surface-electrode ion traps [PLB + 06]. Although this was a useful experiment for prototyping multiplexed surface-electrode traps, the experimental conditions were very different from those for atomic ions. To reiterate a bit from Sec. 5.5, vacuum is not required, and in fact an ambient air pressure actually increases the stability region for stable trapping. Also, a stable laser source is not needed, as the laser light scatters incoherently from the trapped particles. Our group subsequently demonstrated the first use of PCB traps for trapping atomic ions. Our work on PCB traps has focused on methods for loading the traps, as well as confirming basic properties (e.g. motional frequencies) of the traps. With one trap, we used traditional electron gun loading combined with a helium buffer gas to trap in a PCB trap, then performed micromotion compensation on a fairly large sample of ions [BCL + 07]. In the second experiment, we used laser ablation to directly load a smaller PCB ion trap [LCL + 07]. These experiments are the subject of the remainder of this chapter. 6.2 Design and construction of a planar PCB ion trap The first PCB trap to be loaded with atomic ions, dubbed “San Quentin” by our group, was designed to be a surface-electrode version of a linear ion trap. A diagram of the trap electrodes is shown in Fig. 6-2. The trap follows a five-rod design, in which ions are trapped above a grounded center electrode which has rf electrodes on either side of it that are separated from it by a gap that is milled out of the PCB substrate. The side electrodes 132
Figure 6-2: Layout of the trap electrodes for San Quentin, each labeled with the voltage applied. All voltages except Vrf are dc. A coordinate axis is also supplied; the vantage point in this figure is from the positive ˆy axis, or above the trap. are segmented and are held at carefully-chosen dc potentials. These electrodes both provide confinement along the trap axis and compensate for stray dc fields. Some compensation must be done even in the absence of stray fields, since the endcap electrodes have field components not only along ˆz, the trap axis, but also along ˆy, which is defined to be the vertical direction as noted in the figure. Also, optionally, a “top plate” is positioned above the ion trap with a hole cut for fluorescence imaging. It is often grounded but may hold a dc voltage Vtop. Such an electrode was used in the macroion, but not the 88 Sr + ion, experiments reported in Sec. 5.5. 6.2.1 Modeling the trap The trap is modeled using the CPO software that was discussed also in Ch. 5. The method is to calculate the static potentials that result from voltages on the rf electrodes, then apply the pseudopotential approximation (Eq. 4.8) to them. To this pseudopotential is added the potential resulting from static voltages on the dc electrodes. Typical rf voltages of Vrf = 500-1200 V were applied at Ω/(2π) = 7.6 MHz. This rf drive frequency may take a range of values; normally a suitable range of values is found from simulations and the exact frequency used depends on the rf properties of the combined resonator-trap system, which is difficult to exactly predict ahead of time. Other typical voltages were V2 = 110 V, V3 = 50 V, and V4 = V5 = 0. Surface-electrode traps have the unique property compared to 3-D Paul traps that the trap depth can be increased by applying a voltage Vtop to the top plate. With this increase 133
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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
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 and 114: weeks. Low pressures depend on choo
Page 115 and 116: Figure 5-5: Left: Level diagram for
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: Figure 6-1: Schematic of a linear i
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 and 180: Figure 7-21: The two internal lense
Page 181 and 182: 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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