Keldysh Field Theory for Driven Open Quantum Systems I Theoretical
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The Theory of Quantum Coherence María García Díaz
ADVERTIMENT. Lʼaccés als continguts dʼaquesta tesi queda condicionat a lʼacceptació de les condicions dʼús establertes per la següent llicència Creative Commons: http://cat.creativecommons.org/?page_id=184 ADVERTENCIA. El acceso a los contenidos de esta tesis queda condicionado a la aceptación de las condiciones de uso establecidas por la siguiente licencia Creative Commons: http://es.creativecommons.org/blog/licencias/ WARNING. The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Universitat Aut`onomade Barcelona The theory of quantum coherence by Mar´ıaGarc´ıaD´ıaz under supervision of Prof. Andreas Winter A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in Unitat de F´ısicaTe`orica:Informaci´oi Fen`omensQu`antics Departament de F´ısica Facultat de Ci`encies Bellaterra, December, 2019 “The arts and the sciences all draw together as the analyst breaks them down into their smallest pieces: at the hypothetical limit, at the very quick of epistemology, there is convergence of speech, picture, song, and instigating force.” Daniel Albright, Quantum poetics: Yeats, Pound, Eliot, and the science of modernism Abstract Quantum coherence, or the property of systems which are in a superpo- sition of states yielding interference patterns in suitable experiments, is the main hallmark of departure of quantum mechanics from classical physics. Besides its fascinating epistemological implications, quantum coherence also turns out to be a valuable resource for quantum information tasks, and has even been used in the description of fundamental biological processes. -
The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics
The Union of Quantum Field Theory and Non-equilibrium Thermodynamics Thesis by Anthony Bartolotta In Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 Defended May 24, 2018 ii c 2018 Anthony Bartolotta ORCID: 0000-0003-4971-9545 All rights reserved iii Acknowledgments My time as a graduate student at Caltech has been a journey for me, both professionally and personally. This journey would not have been possible without the support of many individuals. First, I would like to thank my advisors, Sean Carroll and Mark Wise. Without their support, this thesis would not have been written. Despite entering Caltech with weaker technical skills than many of my fellow graduate students, Mark took me on as a student and gave me my first project. Mark also granted me the freedom to pursue my own interests, which proved instrumental in my decision to work on non-equilibrium thermodynamics. I am deeply grateful for being provided this priviledge and for his con- tinued input on my research direction. Sean has been an incredibly effective research advisor, despite being a newcomer to the field of non-equilibrium thermodynamics. Sean was the organizing force behind our first paper on this topic and connected me with other scientists in the broader community; at every step Sean has tried to smoothly transition me from the world of particle physics to that of non-equilibrium thermody- namics. My research would not have been nearly as fruitful without his support. I would also like to thank the other two members of my thesis and candidacy com- mittees, John Preskill and Keith Schwab. -
Keldysh Field Theory for Dissipation-Induced States of Fermions
CORE Metadata, citation and similar papers at core.ac.uk Provided by Electronic Thesis and Dissertation Archive - Università di Pisa Department of Physics Master Degree in Physics Curriculum in Theoretical Physics Keldysh Field Theory for dissipation-induced states of Fermions Master Thesis Federico Tonielli Candidate: Supervisor: Federico Tonielli Prof. Dr. Sebastian Diehl University of Koln¨ Graduation Session May 26th, 2016 Academic Year 2015/2016 UNIVERSITY OF PISA Abstract Department of Physics \E. Fermi" Keldysh Field Theory for dissipation-induced states of Fermions by Federico Tonielli The recent experimental progress in manipulation and control of quantum systems, together with the achievement of the many-body regime in some settings like cold atoms and trapped ions, has given access to new scenarios where many-body coherent and dissipative dynamics can occur on an equal footing and the generators of both can be tuned externally. Such control is often guaranteed by the toolbox of quantum optics, hence a description of dynamics in terms of a Markovian Quantum Master Equation with the corresponding Liouvillian generator is sufficient. This led to a new state preparation paradigm where the target quantum state is the unique steady state of the engineered Liouvillian (i.e. the system evolves towards it irrespective of initial conditions). Recent research addressed the possibility of preparing topological fermionic states by means of such dissipative protocol: on one hand, it could overcome a well-known difficulty in cooling systems of fermionic atoms, making easier to induce exotic (also paired) fermionic states; on the other hand dissipatively preparing a topological state allows us to discuss the concept and explore the phenomenology of topological order in the non-equilibrium context. -
Arxiv:2103.12042V3 [Quant-Ph] 25 Jul 2021 Approximation)
Unified Gorini{Kossakowski{Lindblad{Sudarshan quantum master equation beyond the secular approximation Anton Trushechkin1, 2 1Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia 2National University of Science and Technology MISIS, Moscow 119049, Russia∗ (Dated: July 27, 2021) Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini{Kossakowski{ Lindblad{Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case. I. INTRODUCTION particular, does not preserve positivity of the density op- erator, thus leading to unphysical predictions. Also, this Quantum master equations are at the heart of theory of equation does not have the mentioned thermodynamic open quantum systems [1{3]. They describe the dynam- properties. ics of the reduced density operator of a system interact- Derivation of a mathematically correct quantum mas- ing with the environment (\bath") and are widely used ter equation which takes into account nonsecular effects in quantum optics, condensed matter physics, charge and is actively studied. Several heuristic approaches turning energy transfer in molecular systems, bio-chemical pro- the Redfield equation into an equation of the GKLS form cesses [4], quantum thermodynamics [5,6], etc. -
Quantum-Zeno Fermi Polaron in the Strong Dissipation Limit
PHYSICAL REVIEW RESEARCH 3, 013086 (2021) Quantum-Zeno Fermi polaron in the strong dissipation limit Tomasz Wasak ,1 Richard Schmidt,2 and Francesco Piazza1 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany 2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany (Received 20 January 2020; accepted 24 December 2020; published 28 January 2021) The interplay between measurement and quantum correlations in many-body systems can lead to novel types of collective phenomena which are not accessible in isolated systems. In this work, we merge the Zeno paradigm of quantum measurement theory with the concept of polarons in condensed-matter physics. The resulting quantum-Zeno Fermi polaron is a quasiparticle which emerges for lossy impurities interacting with a quantum-degenerate bath of fermions. For loss rates of the order of the impurity-fermion binding energy, the quasiparticle is short lived. However, we show that in the strongly dissipative regime of large loss rates a long-lived polaron branch reemerges. This quantum-Zeno Fermi polaron originates from the nontrivial interplay between the Fermi surface and the surface of the momentum region forbidden by the quantum-Zeno projection. The situation we consider here is realized naturally for polaritonic impurities in charge-tunable semiconductors and can be also implemented using dressed atomic states in ultracold gases. DOI: 10.1103/PhysRevResearch.3.013086 I. INTRODUCTION increasing the measurement rate of a closed quantum many- body system, a phase transition from a volume-law entangled The effect of measurement on the time evolution of a phase to a quantum Zeno phase with area-law entanglement system is one of the most puzzling aspects of quantum dy- can take place [11,13]. -
Charge and Energy Transfer Processes: Open Problems in Open Quantum Systems
CHARGE AND ENERGY TRANSFER PROCESSES: OPEN PROBLEMS IN OPEN QUANTUM SYSTEMS Aaron Kelly (Dalhousie), Marco Merkli (Memorial), Dvira Segal (Toronto) Aug 18 - Aug 23, 2019 1 Overview of the Field Open quantum systems. A quantum system subjected to external influences is said to be open. The external degrees of freedom are often referred to as an environment, a bath, a reservoir or simply a noise. Typical examples of open quantum systems cover artificial and natural systems including a register of qubits (the system) in contact with a substrate they are mounted on (the environment), or a molecule undergoing a chemical reaction while immersed in a sea of surrounding substances (the solvent) influencing the process. Moreover, in large molecules the electrons and nuclear coordinates that do not directly take part in the reaction may act as a reservoir for the reaction coordinate(s). An open system may experience phase loss, energy and particle exchange with the surroundings, thus being open drastically impacts its dynamics. As even slight external influences can change the evolution of a quantum system considerably, it is important, both from a theoretical and practical standpoint, to be able to model and analyze such interactions. The study of open quantum systems is an important part of modern science. It carries a direct impact on different areas, such as the development of energy conversion and storage technologies based on organic or biological molecules and the realization of quantum-based technologies. According to the postulates of quantum mechanics, the dynamical equation of a closed quantum system (not subjected to an external noise) is the Schrodinger¨ equation, a differential equation governing the time evolution of the wave function (the state) of a system. -
Keldysh Approach for Nonequilibrium Phase Transitions in Quantum Optics: Beyond the Dicke Model in Optical Cavities
Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Torre, Emanuele, Sebastian Diehl, Mikhail Lukin, Subir Sachdev, and Philipp Strack. 2013. “Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities.” Physical Review A 87 (2) (February 21). doi:10.1103/ PhysRevA.87.023831. http://dx.doi.org/10.1103/PhysRevA.87.023831. Published Version doi:10.1103/PhysRevA.87.023831 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11688797 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities 1, 2, 3 1 1 1 Emanuele G. Dalla Torre, ⇤ Sebastian Diehl, Mikhail D. Lukin, Subir Sachdev, and Philipp Strack 1Department of Physics, Harvard University, Cambridge MA 02138 2Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria 3Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria (Dated: January 16, 2013) We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an e↵ective temperature set by the atom-photon interaction strength. -
Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime
Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime Alessio Settineri,1 Vincenzo Macr´ı,2 Alessandro Ridolfo,2 Omar Di Stefano,2 Anton Frisk Kockum,2, 3 Franco Nori,2, 4 and Salvatore Savasta1, 2 1Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit`adi Messina, I-98166 Messina, Italy 2Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan 3Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden 4Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA (Dated: November 22, 2018) arXiv:1807.06348v3 [quant-ph] 21 Nov 2018 1 Abstract The interaction among the components of a hybrid quantum system is often neglected when con- sidering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical predictions, as has been shown for cavity-QED and optomechanical systems in the ultrastrong-coupling regime. To deal with these cases, master equations with dissipators retaining the interaction between these components have been derived for the quantum Rabi model and for the standard optomechanical Hamiltonian. In this article, we go beyond these previous derivations and present a general master equation approach for arbi- trary hybrid quantum systems interacting with thermal reservoirs. Specifically, our approach can be applied to describe the dynamics of open hybrid systems with harmonic, quasi-harmonic, and anharmonic transitions. We apply our approach to study the influence of temperature on multipho- ton vacuum Rabi oscillations in circuit QED. -
Coding Closed and Open Quantum Systems in MATLAB: Applications in Quantum Optics and Condensed Matter
Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter Ariel Norambuena1, Diego Tancara2, and Ra´ulCoto1 1 Centro de Investigaci´onDAiTA Lab, Facultad de Estudios Interdisciplinarios, Universidad Mayor, Chile 2 Faculty of Physics, Pontificia Universidad Cat´olicade Chile, Avda. Vicu~na Mackenna 4860, Santiago, Chile E-mail: [email protected] Abstract. We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high background in MATLAB, and also for researches interested in numerical studies applied to quantum optics and condensed matter systems. 1. Introduction Myriad current research fields in quantum optics and condensed matter demand numerical analysis of complex many-body systems (MBS). Interesting effects like arXiv:1911.04906v2 [quant-ph] 27 Feb 2020 dynamical quantum phase transition (DQPT), meta-stability, steady states, among others, can naturally emerge in MBS. These effects are observed in closed decoherence- free dynamics such as the Jaynes-Cummings [1], Jaynes-Cummings-Hubbard [2], trapped ions [3], cavity opto-mechanics [4] or Ising models [5]. Furthermore, for open quantum systems, the environment may cause memory effects in the reservoir time scale, which is known as non-Markovianity (NM) [6, 7]. -
From the Keldysh Formalism to the Boltzmann Equation for Spin Drift and Diffusion
Ismael Ribeiro de Assis From the Keldysh formalism to the Boltzmann equation for spin drift and diffusion Uberlândia, Minas Gerais, Brasil 29 de julho de 2019 Ismael Ribeiro de Assis From the Keldysh formalism to the Boltzmann equation for spin drift and diffusion Dissertação apresentada ao Programa de Pós- graduação em Física da Universidade Fed- eral de Uberlândia, como requisito parcial para obtenção do título de mestre em Física Teórica. Área de Concentração: Física da Matéria Condensada. Universidade Federal de Uberândia – UFU Insituto de Física - INFIS Programa de Pós-Graduação Orientador: Prof. Dr. Gerson Ferreira Junior Uberlândia, Minas Gerais, Brasil 29 de julho de 2019 Ficha Catalográfica Online do Sistema de Bibliotecas da UFU com dados informados pelo(a) próprio(a) autor(a). A848 Assis, Ismael Ribeiro de, 1994- 2019 From the Keldysh formalism to the Boltzmann equation for spin drift and diffusion [recurso eletrônico] / Ismael Ribeiro de Assis. - 2019. Orientador: Gerson Ferreira Júnior. Dissertação (Mestrado) - Universidade Federal de Uberlândia, Pós-graduação em Física. Modo de acesso: Internet. Disponível em: http://dx.doi.org/10.14393/ufu.di.2019.2247 Inclui bibliografia. 1. Física. I. Ferreira Júnior, Gerson , 1982-, (Orient.). II. Universidade Federal de Uberlândia. Pós-graduação em Física. III. Título. CDU: 53 Bibliotecários responsáveis pela estrutura de acordo com o AACR2: Gizele Cristine Nunes do Couto - CRB6/2091 Nelson Marcos Ferreira - CRB6/3074 Dedico à minha família Acknowledgements Gostaria de agradecer as pessoas próximas que fazem com que minha carreira seja possível. Especialmente minha família, minha mãe June, meu pai Anísio e minha irmã Geovana, que durante os anos desta jornada tem me apoiado emocionalmente e financeiramente. -
Quantum Correlations and Quantum Coherence in Open Quantum Systems
Paola Andrea Concha Obando QUANTUM CORRELATIONS AND QUANTUM COHERENCE IN OPEN QUANTUM SYSTEMS Brasil 2018 Paola Andrea Concha Obando QUANTUM CORRELATIONS AND QUANTUM COHERENCE IN OPEN QUANTUM SYSTEMS Tese apresentada ao Curso de Pós-Graduação em Física da Universidade Federal Flumi- nense, como requisito parcial para obtenção do Título de Doutor em Física. Universidade Federal Fluminense Instituto de Física Programa de Pós-Graduação Orientador Prof. Dr. Marcelo Silva Sarandy Coorientador Prof. Dr. Fagner Muruci de Paula Brasil 2018 Paola Andrea Concha Obando QUANTUM CORRELATIONS AND QUANTUM COHERENCE IN OPEN QUAN- TUM SYSTEMS/ Paola Andrea Concha Obando. – Brasil, 2018- 141 p. : il. (algumas color.) ; 30 cm. Orientador: Prof. Dr. Marcelo Silva Sarandy Co-Orientador: Prof. Dr. Fagner Muruci de Paula Tese (Doutorado) – Universidade Federal Fluminense Instituto de Física Programa de Pós-Graduação, 2018. 1. Decoherence, open systems. 2. quantum statistical methods. 2. quantum information.. I. Dr. Marcelo Silva Sarandy II. Universidade Federal Fluminense. III. Programa de Física. IV. Título A mi vida y a mi madre. ACKNOWLEDGEMENTS Os meus agradecimentos são em primeiro lugar para o meu orientador Marcelo Sarandy, pelo seu tempo, paciência, dedicação e ensinamentos. Sem dúvidas uma grande pessoa e por quem tenho uma profunda admiração. Para mim, foi um enorme privilégio trabalhar sobre a sua orientação durante estes quatro anos e espero poder contar com a sua colaboração e amizade no futuro. Agradeço ao meu co-orientador Fagner Muruci de Paula, obrigada pela sua amizade, as suas valiosas ideias, pelas discussões e pelos trabalhos em conjunto. Agradeço a minha família por estar sempre comigo sem importar a distância, a meus pais que me apoiaram nesta decisão, a minha irmã Jenny por compartilhar o amor pela física e nosso trabalho em conjunto. -
Lindblad Driving for Nonequilibrium Steady-State Transport for Noninteracting Quantum Impurity Models
Lindblad driving for nonequilibrium steady-state transport for noninteracting quantum impurity models Matthias Bauer München 2011 Lindblad driving for nonequilibrium steady-state transport for noninteracting quantum impurity models Matthias Bauer Bachelorarbeit an der Fakultät für Physik der Ludwig–Maximilians–Universität München vorgelegt von Matthias Bauer aus Baden-Baden München, den 26. Juli 2011 Gutachter: Prof. Dr. Jan von Delft Contents Abstract vii 1. Introduction 1 2. Prerequisites 3 2.1. Unitary Evolution of Closed Quantum Systems . .3 2.2. Schrödinger, Heisenberg and Interaction Picture . .4 2.3. Fermionic Creation and Annihilation Operators . .5 3. Quantum Master Equations 7 3.1. Open Quantum Systems . .7 3.2. Time Evolution and Dynamical Maps . .8 3.3. The Lindblad Quantum Master Equation . 10 4. General Derivation from Microsopic Models 13 4.1. Properties of the Baths . 13 4.2. Projection Operator Method . 14 4.3. Bath Correlation Functions . 16 4.4. The Markov Approximation . 17 5. The Resonant Level Model 19 5.1. Description of the Model . 19 5.2. Quantum Master Equation . 19 5.3. Equilibrium Properties: Thermalization Behavior . 21 6. Two Coupled Levels, one Bath 23 6.1. Quantum Master Equation in the Eigenbasis . 24 6.2. Quantum Master Equation in the Local Basis . 27 6.3. Comparison . 27 6.4. Discussion of the Born-Markov Approximation . 30 7. Two Coupled Levels with two Taths 33 7.1. Exact Current using Keldysh Formalism . 34 7.2. QME in the Eigenbasis . 36 7.3. QME in the Local Basis . 38 7.4. Comparison . 38 8. Aharanov-Bohm like Problems 45 8.1.