Dephasing and Decoherence in Open Quantum Systems: A Dyson's Equation Approach Item Type text; Electronic Dissertation Authors Cardamone, David Michael Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 01/10/2021 17:26:52 Link to Item http://hdl.handle.net/10150/195386 Dephasing and Decoherence in Open Quantum Systems: A Dyson's Equation Approach by David Michael Cardamone A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHYSICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2 0 0 5 3 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by David M. Cardamone entitled Dephasing and Decoherence in Open Quantum Systems: A Dyson's Equation Approach and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy Date: 08/04/05 Bruce R. Barrett Date: 08/04/05 Charles A. Stafford Date: 08/04/05 Sumitendra Mazumdar Date: 08/04/05 Michael A. Shupe Date: 08/04/05 Koen Visscher Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copies of the dissertation to the Graduate College. We hereby certify that we have read this dissertation prepared under our direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 08/04/05 Dissertation Director: Bruce R. Barrett Date: 08/04/05 Dissertation Director: Charles A. Stafford 4 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, pro- vided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: David Michael Cardamone 5 ACKNOWLEDGEMENTS From the bottom of my heart, the greatest thanks I have must go to my wife, Martha. Through the years, she has been an unparalleled source of love, hope, advice, support, and friendship. Her wisdom has informed each choice I have made, and her example has inspired me. Thank you, Martha. I must also thank my parents and grandparents, who provided me with a safe child- hood, allowed me the luxury of exploring my own interests, and, above all, gave me their confidence. By their example, they taught me a sense of personal responsibility, ethics, and morality, which shaped the person I have become. On a final personal note, I do not want to forget my friends in Tucson who have helped me in numerous ways over the years. I was fortunate to travel professionally quite a bit during my grad student years, and James Little, Geoff Schmidt, and Jeremy Jones facilitated this in all those important ways that friends do. I also thank Tucson Kendo Kai for helping me find the determination, courage, and character necessary to a grad student's lifestyle. On the professional side, I could not have been more honored or fortunate to work under the tutelage and supervision of Profs. Bruce Barrett and Charles Stafford. They, too, gave me their confidence. Much more useful than teaching me physics (although they did that as well), they showed me how to learn physics. I shall never forget their tireless efforts to guide me on the long journey from inexperienced student to practicing physicist. An additional very special thanks is due to Prof. Sumit Mazumdar, with whom I have also had the privilege of collaborating the last two years. Although Sumit had many answers, equally valuable in this collaboration were his questions. He took the time to give excellent and thoughtful career advice, which was key in getting me where I am today. Indeed, the entire community of the University of Arizona Department of Physics have been welcoming and helpful to me during my time here. Over the years, my thesis committee, including those mentioned above as well as Profs. Mike Shupe, Koen Visscher, and Srin Manne, have always found time to help me with advice or encouragement. So too have the other faculty of the department, including especially Keith Dienes, Fulvio Melia, Jan Refelski, Bob Thews, Bira van Kolck, J. D. Garcia, and Carlos Bertulani. Among all the helpful staff, Mike Eklund and Phil Goisman always went above and beyond the call of duty without complaint, for which I wish to express my appreciation and admiration. My understanding of the scientific issues discussed in this work has benefitted enor- mously from numerous engaging discussions over the years. In particular, thanks are due to Chang-hua Zhang, Jerome Burki,¨ Jeremie Korta, Ned Wingreen, Peter von Brentano, Micah Johnson, Ryoji Okamoto, Dan Stein, Anna Wilson, Paul Davidson, Mahir Hussein, Adam Sargeant, and George Kirczenow. The pleasure of discussion and collaboration with such outstanding physicists is one I hope will continue for many years. 6 For Martha, meae vitae. 7 TABLE OF CONTENTS LIST OF FIGURES . 10 LIST OF TABLES . 12 ABSTRACT . 13 CHAPTER 1: INTRODUCTION . 14 1.1 Green Functions . 15 1.1.1 General theory of Green functions . 16 1.1.2 Electrostatic Green functions . 18 1.1.3 Quantum mechanical Green functions . 19 1.2 Physical Systems . 20 1.2.1 Coupled quantum dots . 21 1.2.2 Decay of superdeformed nuclei . 21 1.2.3 Molecular electronics . 22 CHAPTER 2: DYSON'S EQUATION . 23 2.1 Derivation . 23 2.1.1 S-matrix expansion . 23 2.1.2 Diagrammatic approach . 26 2.2 Self-Energies . 29 2.2.1 Hybridization: adding a second level . 30 2.2.2 Decoherence: a single continuum . 31 2.3 Summary . 33 CHAPTER 3: COUPLED QUANTUM DOTS . 34 3.1 Quantum Dots . 35 3.1.1 History and fabrication . 36 3.1.2 Experimental studies . 37 3.2 Two-Level Model . 38 3.2.1 Realm of Applicability to Quantum Dots . 39 8 TABLE OF CONTENTS {Continued 3.2.2 Hamiltonian of the coupled dot system . 39 3.2.3 Spin-boson analogy . 41 3.3 Green Function Treatment . 42 3.3.1 Without leads . 43 3.3.2 Including the leads . 45 3.4 Limiting Cases . 48 3.4.1 Identical dots . 49 3.4.2 Identical lead couplings . 50 3.5 Summary . 50 CHAPTER 4: DECAY OF SUPERDEFORMED NUCLEI . 52 4.1 Nuclear Deformation . 52 4.1.1 Normal deformation . 53 4.1.2 Superdeformation . 56 4.1.3 Experimental signatures of deformation . 57 4.2 Decay Process . 60 4.2.1 Experiments . 60 4.2.2 Double-well paradigm . 63 4.3 Two-State Model . 65 4.3.1 Two-state Hamiltonian . 66 4.3.2 Energy broadenings . 67 4.3.3 Green function treatment . 70 4.3.4 Branching ratios . 70 4.4 Tunneling Width . 72 4.4.1 Relation between branching ratios and tunneling width . 72 4.4.2 Measurement of the tunneling width . 73 4.4.3 Limits of the tunneling width . 75 4.5 Statistical Theory of Tunneling . 76 4.5.1 Gaussian orthogonal ensemble . 76 4.5.2 Implications for tunneling . 77 9 TABLE OF CONTENTS {Continued 4.6 Adding More Levels . 80 4.6.1 Three-state model . 80 4.6.2 Infinite-band approximation . 84 4.7 Summary . 86 CHAPTER 5: MOLECULAR ELECTRONICS . 88 5.1 Fabrication of Single-Molecular Systems . 88 5.1.1 Scanning-tunneling microscopic techniques . 89 5.1.2 Mechanically controllable break junction . 90 5.1.3 Other techniques . 92 5.2 Modeling Molecular Electronics . 92 5.2.1 Hamiltonian . 93 5.2.2 Hartree-Fock approximation . 95 5.2.3 Non-equilibrium Green function theory . 95 5.2.4 Equal-time correlation functions . 98 5.2.5 Landauer-Buttik¨ er formalism . 99 5.3 Quantum Interference Effect Transistor . 101 5.3.1 Tunable conductance suppression . 101 5.3.2 Finite voltage . 105 5.4 Summary . 108 CHAPTER 6: DISCUSSION . 109 REFERENCES . 111 10 LIST OF FIGURES 2.1 Dyson's equation expansion of the full retarded self-energy Σ? . 28 3.1 Electron micrograph images of experimental quantum dots . 36 3.2 Experimental spectra and addition energies of quantum dots . 38 3.3 Schematic diagram of the double quantum dot system . 40 3.4 Hybridization of energy levels in the double-dot system without leads . 43 3.5 Coherent Rabi oscillations in the double-dot system without leads . 45 3.6 Mixture of coherent and incoherent behavior in the full system . 47 4.1 Evidence for shell closures in the first excited state of even-even nuclei . 54 4.2 Evidence for shell closures in nuclear separation energies . 54 4.3 Normal deformation and superdeformation on the table of nuclides . 56 4.4 Superdeformation from a harmonic oscillator potential . 58 4.5 Decay spectrum of superdeformed 152Dy . 61 4.6 Universality in the decay of superdeformed nuclei of A 190 . 62 ≈ 4.7 Diagram of the superdeformed decay process . 63 4.8 Types of potentials historically used to model superdeformed decay .