DOCSLIB.ORG

Partial Measurements of Quantum Systems by Jonathan Tyler Monroe

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Partial Measurements of Quantum Systems by Jonathan Tyler Monroe WASHINGTON UNIVERSITY IN ST.LOUIS Department of Physics Dissertation Examination Committee: Kater Murch, Chair James Buckley Erik Henriksen Zohar Nussinov Jung-Tsung Shen Partial Measurements of Quantum Systems by Jonathan Tyler Monroe A dissertation presented to The Graduate School of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2021 St. Louis, Missouri © 2021, Jonathan Tyler Monroe Table of Contents List of Figures........................................................................................... v List of Tables ............................................................................................ vii Acknowledgments...................................................................................... viii Abstract ................................................................................................... xi Chapter 1: Introduction............................................................................ 1 1.1 Motivation....................................................................................... 1 1.2 Quantum Mechanics with Circuits ........................................................ 4 1.2.1 Quantizing the cavity............................................................... 4 1.2.2 Quantizing the LC Circuit ........................................................ 7 1.2.3 Quantizing the Nonlinear LC ..................................................... 8 1.3 Readout Physics ............................................................................... 9 1.3.1 Jaynes-Cummings Interaction .................................................... 10 1.3.2 Partial Measurements............................................................... 14 Chapter 2: Direct-Write Qubits ................................................................ 18 2.1 Introduction..................................................................................... 18 2.2 Fabrication Theory............................................................................ 20 2.2.1 Josephson Junction Nonlinearity ................................................ 20 2.2.2 Josephson Relations from BCS Theory ........................................ 22 2.2.3 Cabrera-Mott Oxidation Model .................................................. 23 2.3 Recipe Development .......................................................................... 28 2.3.1 Design-of-Experiment Philosophy ............................................... 28 2.3.2 Resist Exposure Tuning............................................................ 29 2.3.3 Junction Consistency Tests ....................................................... 35 ii 2.3.4 Full Recipe ............................................................................ 39 2.4 Devices........................................................................................... 43 2.4.1 Structure of Large-Area Junctions .............................................. 44 2.4.2 Circuit Spectroscopy ................................................................ 48 2.4.3 Time Domain Measurements ..................................................... 52 2.4.4 Additional Noise Sources .......................................................... 56 2.4.5 Limits on Loss Tangents ........................................................... 57 Chapter 3: Entropic Uncertainty Relations ............................................... 58 3.1 Introduction..................................................................................... 58 3.1.1 Problems with Variance-based Uncertainty Relations ...................... 59 3.1.2 Entropic Uncertainty Relations .................................................. 60 3.2 Theory............................................................................................ 63 3.2.1 Trivial Bound ......................................................................... 64 3.2.2 Deutsch Bound ....................................................................... 65 3.2.3 Maassen-Uffink Bound ............................................................. 66 3.2.4 Tomamichel Bound.................................................................. 67 3.2.5 Weak Measurement Bound ........................................................ 67 3.3 Experiment...................................................................................... 70 3.3.1 Entropies of the Entropic Uncertainty Relation ............................. 71 3.3.2 Bound of the Entropic Uncertainty Relation ................................. 81 3.3.3 Combing Elements of the RHS ................................................... 85 Chapter 4: Time-Reversed Feedback ......................................................... 88 4.1 Introduction..................................................................................... 88 4.2 Stochastic Thermodynamics ................................................................ 90 4.2.1 Classical Fluctuation Theorems.................................................. 90 4.2.2 Thermodynamics of Quantum Trajectories ................................... 96 4.3 Experiment...................................................................................... 98 4.3.1 Setup.................................................................................... 98 4.3.2 Trajectory probabilities ............................................................ 101 4.3.3 Fluctuation Theorems .............................................................. 103 iii 4.4 Conclusion....................................................................................... 107 Bibliography ............................................................................................. 108 iv List of Figures Figure 1.1: Jaynes-Cummings Hamiltonian Eigenenergies ............................... 12 Figure 2.1: Cabrera Theory...................................................................... 26 Figure 2.2: Exposure Test for S1805........................................................... 30 Figure 2.3: Resist Stack Imaging ............................................................... 32 Figure 2.4: Codename Sandwich Factorial Design ......................................... 33 Figure 2.5: Resistance Variation from Area Variation .................................... 35 Figure 2.6: Variation in Manhattan Evaporation .......................................... 36 Figure 2.7: Wafer Variation with Improved Softbaking................................... 38 Figure 2.8: SEM image of a Large-area Junction .......................................... 44 Figure 2.9: Preparing TEM Sample ........................................................... 45 Figure 2.10: EDXS Data for Multi-layer Junction........................................... 46 Figure 2.11: Resistance Scaling with Oxide Thickness ..................................... 47 Figure 2.12: High Power Spectroscopy ......................................................... 49 Figure 2.13: TLS in Spectroscopy ............................................................... 51 Figure 2.14: T1 vs Flux and Time ............................................................... 53 Figure 2.15: Quality Factor Histograms........................................................ 55 Figure 2.16: Quality Factor Aging............................................................... 56 Figure 3.1: Pulse sequence for measuring entropies........................................ 71 Figure 3.2: Measurement Angles ............................................................... 72 Figure 3.3: Projective measurement entropies .............................................. 74 Figure 3.4: Entropy in the Presence of Weak Measurement ............................. 76 v Figure 3.5: Entropy Under the Influence of Weak Measurement ....................... 78 Figure 3.6: Entropies of the Entropic Uncertainty Relation ............................. 80 Figure 3.7: RHS Components ................................................................... 82 Figure 3.8: Weak Value Measurement Protocol ............................................ 83 Figure 3.9: Weak Values.......................................................................... 84 Figure 3.10: RHS of Entropic Uncertainty Relation ........................................ 87 Figure 4.1: Readout Distributions ............................................................. 99 Figure 4.2: Correlated Tomography ........................................................... 101 Figure 4.3: Feedback Protocol .................................................................. 105 Figure 4.4: Entropy Histograms ................................................................ 106 vi List of Tables Table 3.1: Select values of H(AF )ρ ........................................................... 81 vii Acknowledgments I am delighted to thank the many people who have guided and supported me during my graduate studies. The bountiful support of those close to me filled my experience with joy. I begin with the central driver of my success: Kater Murch. I count myself exceptionally fortunate to have been mentored by such a personable and passionate advisor as Kater. Kater’s example has instilled the virtue of clear explanations. I feel honored to have worked among such great colleagues in the Murch lab. I thank Dian Tan for his patient tutelage of fabrication techniques and Mahdi Naghiloo for his willing explanation of every aspect of our lab, especially as codified in his dissertation. Patrick Harrington has been
Load more

Recommended publications
  • Elementary Explanation of the Inexistence of Decoherence at Zero
    Elementary explanation of the inexistence of decoherence at zero temperature for systems with purely elastic scattering Yoseph Imry Dept. of Condensed-Matter Physics, the Weizmann Institute of science, Rehovot 76100, Israel (Dated: October 31, 2018) This note has no new results and is therefore not intended to be submitted to a ”research” journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. Several of those have approached the author for his opinion, which is summarized here in a hopefully pedagogical manner, for convenience. It is demonstrated, using essentially only energy conservation and elementary quantum mechanics, that true decoherence by a normal environment approaching the zero-temperature limit is impossible for a test particle which can not give or lose energy. Prime examples are: Bragg scattering, the M¨ossbauer effect and related phenomena at zero temperature, as well as quantum corrections for the transport of conduction electrons in solids. The last example is valid within the scattering formulation for the transport. Similar statements apply also to interference properties in equilibrium. PACS numbers: 73.23.Hk, 73.20.Dx ,72.15.Qm, 73.21.La I. INTRODUCTION cally in the case of the coupling of a conduction-electron in a solid to lattice vibrations (phonons) 14 years ago [5] and immediately refuted vigorously [6]. Interest in this What diminishes the interference of, say, two waves problem has resurfaced due to experiments by Mohanty (see Eq. 1 below) is an interesting fundamental ques- et al [7] which determine the dephasing rate of conduc- tion, some aspects of which are, surprisingly, still being tion electrons by weak-localization magnetoconductance debated.
    [Show full text]
  • Discussion Meeting on Quantum Measurements Centre for Quantum Information and Quantum Computation Indian Institute of Science, Bangalore 22-24 October 2014
    Discussion Meeting on Quantum Measurements Centre for Quantum Information and Quantum Computation Indian Institute of Science, Bangalore 22-24 October 2014 Organizing Committee N.D. Hari Dass CMI, Chennai (Chairman) Dipankar Home Bose Institute, Kolkata Anil Kumar IISc, Bangalore (Convener) T.S. Mahesh IISER, Pune Archan S. Majumdar SNBNCBS, Kolkata Kota Murali IBM, Bangalore Apoorva Patel IISc, Bangalore Arun K. Pati HRI, Allahabad R. Simon IMSc, Chennai Urbasi Sinha RRI, Bangalore Rajamani Vijayaraghavan TIFR, Mumbai Talks 9:30-10:20 22 October 2014 Quantum measurement theory and the uncertainty principle Masanao Ozawa Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya, Japan Heisenberg’s uncertainty principle was originally formulated in 1927 as a quantitative relation between the “mean error” of a measurement of one observable and the “discontinuous change” (or the disturbance) thereby caused on another observ- able, typically explained through the gamma ray microscope thought experiment. Heisenberg derived this relation under an additional assumption on quantum measurements that is consistent with the so-called repeatability hypothesis, which was pos- tulated in von Neumann’s measurement theory and supported by Schroedinger and contemporaries. However, the repeatability hypothesis has been abandoned in the modern quantum measurement theory, originated by Davies and Lewis in the 1970’s. Later, the universal validity of Heisenberg’s uncertainty principle was questioned typically in a debate on the sensitivity limit to gravitational wave detectors in the 1980’s. A universally valid form of the error-disturbance relation was derived in the modern framework for general quantum measurements by the present speaker in 2003. Since then we have experienced a considerable progress in theoretical and experimental studies of universally valid reformulation of Heisenberg’s uncertainty principle.
    [Show full text]
  • An Investigation of No-Go Theorems in Hidden Variable Models of Quantum Mechanics
    An investigation of No-Go theorems in Hidden Variable Models of Quantum Mechanics by Navid Siami BSc. Sharif University of Technology, 2012 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2016 © Navid Siami, 2016 Abstract Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function. ii Preface This body of work by N. Siami is independent and unpublished. iii Table of Contents Abstract ............................................................................................................................................................................................ii Preface ............................................................................................................................................................................................ iii Table of Contents
    [Show full text]
  • Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected]
    Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Science and Technology Faculty Articles and Faculty Articles and Research Research 2016 Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected] Eliahu Cohen Tel Aviv University Tomer Shushi University of Haifa Follow this and additional works at: http://digitalcommons.chapman.edu/scs_articles Part of the Quantum Physics Commons Recommended Citation Aharonov, Y., Cohen, E., & Shushi, T. (2016). Accommodating Retrocausality with Free Will. Quanta, 5(1), 53-60. doi:http://dx.doi.org/10.12743/quanta.v5i1.44 This Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University Digital Commons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorized administrator of Chapman University Digital Commons. For more information, please contact [email protected]. Accommodating Retrocausality with Free Will Comments This article was originally published in Quanta, volume 5, issue 1, in 2016. DOI: 10.12743/quanta.v5i1.44 Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 License. This article is available at Chapman University Digital Commons: http://digitalcommons.chapman.edu/scs_articles/334 Accommodating Retrocausality with Free Will Yakir Aharonov 1;2, Eliahu Cohen 1;3 & Tomer Shushi 4 1 School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. E-mail: [email protected] 2 Schmid College of Science, Chapman University, Orange, California, USA. E-mail: [email protected] 3 H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK.
    [Show full text]
  • Weak Measurement in Quantum Mechanics
    Weak Measurement in Quantum Mechanics Author: Mile Vrbica Mentor: Prof. Anton Ramˇsak April 2020 Abstract This seminar focuses on weak measurement with post-selection that introduces the so-called weak value, which is an experimentally accessible complex quantity that possesses non-intuitive behavior. The general measurement process and with an example is described. Properties of the weak value and its uses are discussed. The experimental support of the theory is provided and its applications are reviewed. 1 Contents 1 Introduction ...................................................................................................................................... 2 2 Quantum Measurement Theory.................................................................................................... 2 2.1 The Setup .................................................................................................................................... 2 2.2 The Interaction ............................................................................................................................ 3 2.3 Weak Measurement...................................................................................................................... 3 2.4 The Stern-Gerlach experiment..................................................................................................... 4 3 Weak Measurement with Post-Selection..................................................................................... 5 3.1 The Weak Value..........................................................................................................................
    [Show full text]
  • Geometric Phase from Aharonov-Bohm to Pancharatnam–Berry and Beyond
    Geometric phase from Aharonov-Bohm to Pancharatnam–Berry and beyond Eliahu Cohen1,2,*, Hugo Larocque1, Frédéric Bouchard1, Farshad Nejadsattari1, Yuval Gefen3, Ebrahim Karimi1,* 1Department of Physics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada 2Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 5290002, Israel 3Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel *Corresponding authors: [email protected], [email protected] Abstract: Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior and later manifestations exist. Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and became increasingly influential in many areas from condensed-matter physics and optics to high energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review we first introduce the Aharonov-Bohm effect as an important realization of the geometric phase. Then we discuss in detail the broader meaning, consequences and realizations of the geometric phase emphasizing the most important mathematical methods and experimental techniques used in the study of geometric phase, in particular those related to recent works in optics and condensed-matter physics. Published in Nature Reviews Physics 1, 437–449 (2019). DOI: 10.1038/s42254-019-0071-1 1. Introduction A charged quantum particle is moving through space.
    [Show full text]
  • 2015 Annual Report
    2015 AMERICAN PHYSICAL SOCIETY ANNUAL TM ADVANCING PHYSICS REPORT TM THE AMERICAN PHYSICAL SOCIETY STRIVES TO Be the leading voice for physics and an authoritative source of physics information for the advancement of physics and the benefit of humanity Collaborate with national scientific societies for the advancement of science, science education, and the science community Cooperate with international physics societies to promote physics, to support physicists worldwide, and to foster international collaboration Have an active, engaged, and diverse membership, and support the activities of its units and members © 2016 American Physical Society During 2015, APS worked to institute the governance objective: “the advancement and diffusion of the knowledge changes approved by the membership in late 2014. In of physics.” APS is fully committed to the principles of OA accordance with the new Constitution & Bylaws, in to the extent that we can continue to support the production February the Board appointed our first Chief Executive of high-quality peer-reviewed journals. For many years APS Officer—Kate Kirby, the former Executive Officer—to has supported “green” OA and we have been fully compliant head the APS. Kate’s major task has been to transition with the 2013 directive from the Office of Science and the management of APS to a CEO model with a Senior Technology Policy that the publications resulting from Management Team. She appointed Mark Doyle as Chief U.S. federally funded research be accessible to the public 12 Information Officer, James Taylor as Chief Operating months after publication. Since APS is a major international Officer, and Matthew Salter as the new Publisher.
    [Show full text]
  • Everettian Probabilities, the Deutsch-Wallace Theorem and the Principal Principle
    Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle Harvey R. Brown and Gal Ben Porath Chance, when strictly examined, is a mere negative word, and means not any real power which has anywhere a being in nature. David Hume (Hume, 2008) [The Deutsch-Wallace theorem] permits what philosophy would hitherto have regarded as a formal impossibility, akin to deriving an ought from an is, namely deriving a probability statement from a factual statement. This could be called deriving a tends to from a does. David Deutsch (Deutsch, 1999) [The Deutsch-Wallace theorem] is a landmark in decision theory. Nothing comparable has been achieved in any chance theory. [It] is little short of a philosophical sensation . it shows why credences should conform to [quantum chances]. Simon Saunders (Saunders, 'The Everett interpretation: probability' [unpublished manuscript]) Abstract This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky's thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason's 1957 theorem in his derivation of the Born Rule. Pitowsky's defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective \chances" is questioned, and the status of David Lewis influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics.
    [Show full text]
  • Annual Report to Industry Canada Covering The
    Annual Report to Industry Canada Covering the Objectives, Activities and Finances for the period August 1, 2008 to July 31, 2009 and Statement of Objectives for Next Year and the Future Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo, Ontario N2L 2Y5 Table of Contents Pages Period A. August 1, 2008 to July 31, 2009 Objectives, Activities and Finances 2-52 Statement of Objectives, Introduction Objectives 1-12 with Related Activities and Achievements Financial Statements, Expenditures, Criteria and Investment Strategy Period B. August 1, 2009 and Beyond Statement of Objectives for Next Year and Future 53-54 1 Statement of Objectives Introduction In 2008-9, the Institute achieved many important objectives of its mandate, which is to advance pure research in specific areas of theoretical physics, and to provide high quality outreach programs that educate and inspire the Canadian public, particularly young people, about the importance of basic research, discovery and innovation. Full details are provided in the body of the report below, but it is worth highlighting several major milestones. These include: In October 2008, Prof. Neil Turok officially became Director of Perimeter Institute. Dr. Turok brings outstanding credentials both as a scientist and as a visionary leader, with the ability and ambition to position PI among the best theoretical physics research institutes in the world. Throughout the last year, Perimeter Institute‘s growing reputation and targeted recruitment activities led to an increased number of scientific visitors, and rapid growth of its research community. Chart 1. Growth of PI scientific staff and associated researchers since inception, 2001-2009.
    [Show full text]
  • What Weak Measurements and Weak Values Really Mean: Reply to Kastner
    Found Phys DOI 10.1007/s10701-017-0107-2 What Weak Measurements and Weak Values Really Mean: Reply to Kastner Eliahu Cohen1 Received: 6 April 2017 / Accepted: 9 June 2017 © The Author(s) 2017. This article is an open access publication Abstract Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experi- mentally clarified the meaning and practical significance of weak measurements, yet in Kastner (Found Phys 47:697–707, 2017), Kastner seems to take us many years back- wards in the the debate, casting doubt on the very term “weak value” and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. (Ann Phys 355:258–268, 2015)in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology (which is indeed interpretational and far more complex than that described by Kastner) and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by (strong) projective measurements, without the need of employing weak measurements.
    [Show full text]
  • Member Services 2018
    AMERICAN PHYSICAL SOCIETY Member Services 2018 JANUARY – DECEMBER 2018 GUIDELINES FOR PROFESSIONAL CONDUCT The Constitution of the American Physical Society states that the objective of the Society shall be the advancement and diffusion of the knowledge of physics. It is the purpose of this statement to advance that objective by presenting ethical guidelines for Society members. Each physicist is a citizen of the community of science. Each shares responsibility for the welfare of this community. Science is best advanced when there is mutual trust, based upon honest behavior, throughout the community. Acts of deception, or any other acts that deliberately compromise the advancement of science, are unacceptable. Honesty must be regarded as the cornerstone of ethics in science. Professional integrity in the formulation, conduct, and report- ing of physics activities reflects not only on the reputations of individual physicists and their organizations, but also on the image and credibility of the physics profession as perceived by scientific colleagues, government and the public. It is important that the tradition of ethical behavior be carefully maintained and transmitted with enthusiasm to future generations. The following are the minimal standards of ethical behavior relating to several critical aspects of the physics profession. Physicists have an individual and a collective responsibility to ensure that there is no compromise with these guidelines. RESEARCH RESULTS The results of research should be recorded and maintained in a form that allows analysis and review. Research data should be immediately available to scientific collaborators. Following publication, the data should be retained for a reasonable period in order to be available promptly and completely to responsible scientists.
    [Show full text]
  • The Beginning of Infinity: Explanations That Transform the World Pdf, Epub, Ebook
    THE BEGINNING OF INFINITY: EXPLANATIONS THAT TRANSFORM THE WORLD PDF, EPUB, EBOOK David Deutsch | 487 pages | 29 May 2012 | Penguin Putnam Inc | 9780143121350 | English | New York, NY, United States The Beginning of Infinity: Explanations That Transform the World PDF Book Every argument includes premises in support of a conclusion, but the premises themselves are left unargued. Nov 12, Gary rated it it was amazing Shelves: science. In other words we must have some form of evidence, and it must be coherent with our other beliefs. Nov 12, Gary rated it it was amazing Shelves: science. I can't say why exactly. It seems more to the point to think of it as something emotive — as the expression of a mood. This will lead to the development of explanatory theories variation , which can then be criticized and tested selection. Accuracy and precision are important standards in our evaluation of explanations; standards that are absent in bad explanations. Every argument includes premises in support of a conclusion, but the premises themselves are left unargued. Deutsch starts with explanations being the basis for knowledge, and builds up basic, hard-to-argue-with principles into convincing monoliths that smash some conventional interpretations of knowledge, science and philosophy to tiny pieces. His reliance on Popper is problematic. I will be re-reading them again until it really sinks in. Evolution, in contrast, represents a good explanation because it not only fits the evidence but the details are hard to vary. Barefoot Season Susan Mallery. But the "Occam's Razor" described by the author is not the one practiced in reality.
    [Show full text]