Ph.D. Thesis - Physics

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implemented with a precision that scales favorably with the number of experiments. We also explore ways of actually implementing quantum simulations in such traps, and in doing so make progress toward the goal of a 2-D analog quantum simulator based on trapped ions. Part III In the third part, we ask: can ion-ion coupling over wires be used to scale up digital and analog ion-trap quantum simulators? Coupling over wires could provide a scalable and switchable connection between the motional states of many trapped ions, leading in principle to a more scalable architecture than the traps discussed in Part II. However, some questions must first be addressed. In this part, we focus on the theoretical problems of calculating the expected coupling rate and decoherence rates, and the experimental problem of measuring how the dc and rf electric fields experienced by a single ion vary with the ion-wire distance. These are essential questions when evaluating the potential of this novel method for scaling up ion trap quantum simulators. In Chapter 8, we present a system consisting of two ions confined in a linear surface- electrode Paul trap, near which a thin conducting wire is positioned. We theoretically analyze the ion-ion coupling mediated by the wire, and determine the coupling rate and some important decoherence rates for certain sets of experimental parameters. This work is also important for establishing constraints on the experiment, such as the fact that the wire must be very well-isolated from both dc and rf paths to ground. In Chapter 9, we present the experimental setup and measurements. We study some aspects of connecting ions over a wire by first understanding the effect that a wire has on a single ion. We examine how the presence of the wire alters the trapping potentials, including both ac contributions from the rf trapping potentials and dc contributions from the static charge on the (electrically floating) wire. These results demonstrate the ability to measure electrical properties of a macroscopic object using an ultrasensitive detector: a single trapped ion. We also discuss progress towards understanding how the motional heating rates of the ion vary with the distance from the ion to the wire. Although for the ion-wire distances achieved in our work to date, the heating rate does not vary systematically with the ion-wire distance, this “negative result” is useful for calculating an upper bound on the ion-wire distance such that the heating rate due to the trap electrodes themselves is not greatly increased by the presence of the wire. The results presented in this part show that the wire-mediated coupling between two ions stored in Paul traps is observable in principle, but that the electrically floating wire strongly affects the potentials that act upon the ion. Ion-ion coupling over a wire is a promising method for scaling up ion trap simulators, but more experimental measurements are required at smaller ion-wire distances, of both the effects of the wire on the trap potentials and of the motional heating rate due to the wire. Following Part III, Chapter 10 contains our conclusions and outlook. 40
1.6 Contributions to this work In this section we present the main contributions of the author and his coworkers to this thesis, and then list the publications that have resulted from this work. 1.6.1 Personal contributions In Part I, I participated in all aspects of the experiment and theoretical modeling. I wrote many of the pulse sequences and experimental automation, as well as analyzing the experimental results. I also wrote many of the simulation programs that predicted the results of the quantum simulation, and helped to pinpoint the sources of divergence between them, including the systematic error. A great deal of work that does not appear in this thesis, such as quantum state tomography to diagnose the sources of decoherence, was also done by me. In Part II, I contributed a variety of work. In the experimental work of Ch. 5, I led the investigation of atomic ions in the lattice trap. I built the vacuum chamber and ion trap in which measurements were taken. I also discovered the poor scaling properties of the lattice trap. I worked with my coauthors to analyze the data, particularly the macroion repulsion data. In the experiments which are described in Ch. 6, my primary contribution was the collection of a large quantity of data for both of the resulting publications. I also helped build the vacuum apparatus and prepare the traps for the ablation experiment and set up the ablation targets and laser. For the work of Ch. 7, I designed and had manufactured the elliptical ion traps, set up a new cryogenic vacuum system for testing them, performed all the measurements on them, and drove the theoretical side of the project as well by suggesting problems I thought important to my undergraduate coworkers. I also contributed to writing and debugging many of the simulation codes. Part III represents a collaboration between the Chuang group at MIT and the Blatt group at the Institut für Quantenoptik und Quanteninformation (IQOQI), located at the University of Innsbruck, Austria. I worked about eight months in total at the IQOQI on the experiment. While I was there, some specific things I accomplished were: completing the setup of the vacuum system, including feedthroughs and calcium oven; the first trapping of ions using a trap brought from MIT; electronics including filter boxes, the rf resonator, and putting together the pulse programmer; preparing the Doppler recooling technique and using it to measure the heating rate of a single ion; and making the first systematic observations of the variation in trap frequency and compensation voltages as a function of the ion-wire distance. While back at MIT, I also contributed much to the analysis of new data. 41
Page 1: An Investigation of Precision and S
Page 5 and 6: Acknowledgments What a long, strang
Page 7: should totally start a band. I also
Page 10 and 11: 2.4 Conclusions and further questio
Page 12 and 13: 7.6.1 Regular array of stationary q
Page 15 and 16: List of Figures 2-1 The CNOT gate i
Page 17: 7-12 Magnetic fields due to a “tr
Page 21 and 22: Chapter 1 Introduction The growth o
Page 23 and 24: 1.1 Quantum information The concept
Page 25 and 26: us whether the target system obeys
Page 27 and 28: Nevertheless, there are a number of
Page 29 and 30: Digital Analog Classical Quantum Sp
Page 31 and 32: electrodes [TKK + 99]. This heating
Page 33 and 34: Digital Analog Classical Quantum Sp
Page 35 and 36: 2. Initialization to a simple fiduc
Page 37 and 38: qubits, and in Ref. [SGA + 05] in t
Page 39: the lattice architecture, we discov
Page 43: 5) Ref. [DLC + 09b] Wiring up trapp
Page 47 and 48: Chapter 2 Quantum simulation using
Page 49 and 50: µN the nuclear magneton, and B0 th
Page 51 and 52: ⎡ ⎤ a 0 0 0 ⎢ ⎥ ⎢ ρ2 =
Page 53 and 54: The same effect as number 2 above i
Page 55 and 56: where V0 is the maximum signal stre
Page 57 and 58: actions that occur between nuclei i
Page 59 and 60: Figure 2-2: The 2,3-dibromothiophen
Page 61: 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
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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
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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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Ph.D. Thesis - Physics

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