Ph.D. Thesis - Physics

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other techniques, including electron impact ionization and photoionization. We also probe some other related practical questions, including how the loading efficiency depends upon the composition of the material that is ablated and upon the ablation laser power, and how the number of ions loaded depends upon the ablation laser power. We also qualitatively discuss the buildup of stray electric charge, relative to other loading methods. Although we present PCB’s here as a step towards development of 2-D arrays, our work on them chronologically precedes the work on the lattice trap of the previous chapter. The traps presented in this work are surface-electrode (purely two-dimensional) versions of the well-known linear ion traps from quantum information research. All the experiments were done in a room-temperature vacuum vessel, and the basic questions on which we focused are how ions might be loaded into such a trap, and what effects the loading methods have on the subsequent trapping potentials. Our work on buffer-gas loading with electron impact ionization into a PCB ion trap was the first demonstration of a PCB ion trap for atomic ions, and was presented in Ref. [BCL + 07]. Our work, following this, on laser ablation loading of PCB ion traps, was published as Ref. [LCL + 07]. Following our work, the use of planar PCB ion traps has spread around the world, with traps of our design being used in Innsbruck, Austria, and Osaka, Japan. Additionally, work has been published on the construction of a 3-D segmented linear ion trap from PCB components [HDS + 08], with the goal of creating an extremely accurate single-ion source. The chapter is organized as follows: in Sec. 6.1, we discuss the various prior designs and experiments in surface-electrode ion trapping; in Sec. 6.2, we present the design of our first surface-electrode trap, along with the experimental setup used to study it; in Sec. 6.3, we present the buffer gas loading and micromotion compensation techniques for this trap; in Sec. 6.4, we present the second-generation PCB trap; in Sec. 6.5, we discuss past work in the loading of ion traps using laser ablation, and then present our results using this technique; in Sec. 6.6, we summarize and offer an evaluation of the loading methods presented in this chapter. 6.1 Surface-electrode ion traps: history and theory The “workhorse” of quantum information experiments with trapped ions has been, for the past several years, the linear ion trap. As shown in Fig. 6-1, the trap consists of four long electrodes, on two of which an rf voltage is applied, while the other two are grounded. In this case, “long” means that the length of the electrodes is large compared to the spacing between them. This configuration creates a quadrupole potential; near the center of the trap, this leads to an approximately harmonic time-independent pseudopotential, as discussed in Ch. 4. Confinement along the trap axis, the ˆz direction, is created by a static voltage applied to two endcap electrodes. If the secular frequency in the ˆz direction is small compared to those along ˆx and ˆy, 130
Figure 6-1: Schematic of a linear ion trap. Of four rods, two diagonally opposed rods carry an rf voltage, while the other two are grounded. Confinement along the trap axis is provided by two endcaps that carry a dc voltage. If confinement along the axis is weaker than that along the other two directions, then a linear chain of ions (depicted as blue circles) may be trapped. the ions align in a linear chain along ˆz at the minimum of the pseudopotential. Quantum operations take advantage of the fact that the ions share a common vibrational mode along ˆz. The linear electrodes most frequently have been cylindrically-shaped. An alternative design uses “knife-edge” electrodes; these have the advantage of minimizing the exposure of trapped ions to conducting surfaces. This can lead to a reduction in the motional heating rates of the trapped ions. Despite the numerous achievements made with conventional linear ion traps, they are evidently not scalable, due to the finite number (at most tens) of ions that may be confined along the trap axis. Scaling to larger numbers requires a different approach. As we discussed in Ch. 4, the rate at which quantum gates may be performed is limited by the motional frequency. This frequency is known to scale broadly as the inverse of the trap scale. Thus, a microfabricated trap would enable both a higher density of ions in space and overall higher interaction rates, provided that the ions reside in the same trap region during the interactions. In the case of a digital quantum simulator, microfabricated surface-electrode traps are also conducive to ion shuttling operations between different trap regions. For both analog and digital types, obtaining a higher ion density and coupling rate is advantageous. There are two basic approaches to creating microfabricated ion traps, three-dimensional and two-dimensional (which we refer to as surface-electrode traps). Here we review this distinction. 3-D versions have been designed and constructed by the Wineland group at NIST Boulder [RBKD + 02], the Monroe group at the University of Michigan (now Uni- versity of Maryland) [MHS + 04, SHO + 06], the National <strong>Ph</strong>ysical Laboratory (NPL) of the United Kingdom [BWG + 05], and others. 3-D microfabricated traps have the advantage that generally the trap depth is higher for a given drive voltage and frequency than for comparably-sized 2-D traps. One disadvantage is that fabrication processes are more com- plicated, and that alignment of the different layers of electrodes can be more difficult. 2-D traps, by contrast, contain all trapping electrodes in a single plane. We refer to these traps as surface-electrode ion traps. This idea was first proposed by the Wineland group 131
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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
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
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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 |↑〉
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Page 101 and 102: to the design of the trap itself. M
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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: Chapter 6 Surface-electrode PCB ion
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
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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
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Page 175 and 176: Figure 7-18: At the center of this
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Page 179 and 180: 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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