DOCSLIB.ORG

Many-Body Phenomena in a Bose-Einstein Condensate of Light

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Many-Body Phenomena in a Bose-Einstein Condensate of Light Many-body phenomena in a Bose-Einstein condensate of light Cover: The cover shows an artist's impression of Bose-Einstein condensa- tion of light in a dye-filled optical microcavity. This is inspired by a similar illustration in Physics 7, 7 (2014) (Credit: APS/Alan Stonebraker) ISBN: 978-90-393-6569-4 Printed by Ipskamp Printing Many-body phenomena in a Bose-Einstein condensate of light Veeldeeltjesverschijnselen in een Bose-Einstein condensaat van licht (met een samenvatting in het Nederlands) Proefschrift ter verkrijging van de graad van doctor aan de Universiteit Utrecht op gezag van de rector magnificus, prof. dr. G.J. van der Zwaan, ingevolge het besluit van het college voor promoties in het openbaar te verdedigen op woensdag 22 juni 2016 des middags te 4.15 uur door Arie-Willem de Leeuw geboren op 9 mei 1989 te Leerdam Promotoren: Prof. dr. ir. H.T.C. Stoof Prof. dr. R.A. Duine Contents Publications 7 1 Introduction 11 1.1 Bose-Einstein condensation of atoms . 12 1.2 Driven-dissipative Bose-Einstein condensates . 17 1.3 Bose-Einstein condensation of light . 19 1.4 Outline . 22 2 Schwinger-Keldysh theory 25 2.1 Introduction . 25 2.2 Model . 27 2.3 Non-equilibrium physics . 35 2.4 Equilibrium physics . 40 2.4.1 Normal state . 40 2.4.2 Condensed state . 42 2.5 Conclusion and outlook . 45 3 First-order correlation functions 47 3.1 Introduction . 47 3.2 Phase fluctuations . 49 3.3 Correlation functions in the condensed phase . 53 3.3.1 Spatial correlations . 53 3.3.2 Temporal correlations . 56 3.4 Photons . 57 3.4.1 One-particle density matrix . 57 3.4.2 Normal state . 59 3.5 Conclusion and outlook . 61 6 CONTENTS 4 Number fluctuations 63 4.1 Introduction . 63 4.2 Probability distribution . 65 4.3 Results . 66 4.4 Comparison with experiment . 68 4.5 Photon-photon interaction . 69 4.5.1 Thermal lensing . 69 4.5.2 Dye-mediated photon-photon scattering . 72 4.6 Conclusion . 75 5 Phase diffusion 77 5.1 Introduction . 77 5.2 Quantum fluctuations . 79 5.3 Thermal fluctuations . 83 5.4 Discussion and conclusion . 86 6 Superfluid-Mott-insulator transition 87 6.1 Introduction . 87 6.2 Photonic lattice in dye-filled microcavity . 89 6.3 Mean-field theory . 92 6.3.1 Toy model . 92 6.3.2 Photon model . 97 6.4 Number fluctuations inside the Mott lobes . 99 6.4.1 Quasiparticle excitations . 103 6.4.2 Number fluctuations . 105 6.5 Conclusion and outlook . 110 7 Superfluidity 113 7.1 Introduction . 113 7.2 Semiconductor . 116 7.2.1 Interactions . 118 7.2.2 Scattering length . 121 7.2.3 Many-body effects . 123 7.3 Light in semiconductor microcavities . 126 7.4 Scissors modes . 130 7.5 Damping of scissors modes . 132 7.6 Density-density correlation function . 140 7.7 Discussion and conclusion . 142 Samenvatting 143 7 Curriculum Vitae 148 Acknowledgments 149 Bibliography 152 Publications The main Chapters of this thesis are based on the following papers: A.-W. de Leeuw, H.T.C. Stoof, and R.A. Duine, Schwinger-Keldysh • Theory for Bose-Einstein Condensation of Photons in a Dye-Filled Optical Microcavity, Phys. Rev. A 88, 033829 (2013). A.-W. de Leeuw, H.T.C. Stoof, and R.A. Duine, Phase Fluctuations • and First-Order Correlation Functions of Dissipative Bose-Einstein Condensates, Phys. Rev. A 89, 053627 (2014). E.C.I. van der Wurff, A.-W. de Leeuw, R.A. Duine, and H.T.C. Stoof, • Interaction Effects on Number Fluctuations in a Bose-Einstein Con- densate of Light, Phys. Rev. Lett. 113, 135301 (2014). A.-W. de Leeuw, E.C.I. van der Wurff, R.A. Duine, and H.T.C. Stoof, • Phase Diffusion in a Bose-Einstein Condensate of Light, Phys. Rev. A 90, 043627 (2014). A.-W. de Leeuw, O. Onishchenko, R.A. Duine, and H.T.C. Stoof, • Effects of dissipation on the superfluid-Mott-insulator transition of photons, Phys. Rev. A 91, 033609 (2015). A.-W. de Leeuw, E.C.I. van der Wurff, R.A. Duine, D. van Oosten, • and H.T.C. Stoof, Theory for Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities, submitted for publica- tion in Phys. Rev. A, arXiv:1505.01732. Chapter 1 Introduction In many cases the behavior of objects can be explained by theories within a classical framework. The most famous example is probably the motion of macroscopic masses that is described by Newton's laws. However, it turns out that the behavior of particles at the microscopic level cannot be explained within the same framework. This is a consequence of the different set of rules that must be obeyed on each scale. Namely, at the microscopic level the laws of quantum mechanics apply, which are quite different from the rules of classical mechanics. To distinguish whether quantum mechanics is important or not, we need to compare the average distance between the particles in the system of interest with the thermal de Broglie wavelength of the particles. Here, the latter is defined as s 2π~2 Λth = ; (1.1) mkBT with ~ Planck's constant, m the mass of the particle, kB Boltzmann's con- stant, and T the temperature of the collection of particles in the system. In the regime where this wavelength is smaller than the average distance between the particles, the behavior is classical and the quantum mechanical nature of the particles can be ignored. However, if the de Broglie wave- length becomes larger than the interparticle spacing, or if both quantities are comparable, the effects of the laws of quantum mechanics set in. A prominent example of a many-body phenomenon that is purely quan- tum mechanical is Bose-Einstein condensation (BEC) [1,2]. Based on work of the Indian physicist Bose, Einstein concluded that a nonzero fraction of the number of particles in a gas of bosons occupies the ground state, if the de Broglie wavelength is comparable to the interparticle distance. For the macroscopic occupation of the ground state, the bosonic nature of the particle is crucial, since fermions are not allowed to occupy the 12 1. INTRODUCTION High Energy > > Low Energy Figure 1.1: Schematic picture of evaporative cooling. By reducing the height of the external potential the most energetic atoms are removed from the trap, thereby reducing the average temperature of the trapped atomic gas. same state. At first instance an experimental realization of BEC seemed unrealistic. Namely, for the most convenient bosonic gases, such as rubid- ium and sodium, the maximal densities in experiments are in the range of 1013 1015 cm 3. Therefore, these gases must be cooled to temperatures − − in the nanokelvin regime to observe BEC. 1.1 Bose-Einstein condensation of atoms The key insight for achieving these ultracold temperatures was the notion of the equivalence between the temperature of a gas and the average veloc- ity of the particles of which this gas consists. Namely, reducing the velocity of the particles is equivalent to lowering the temperature of the gas. This is the basic principle behind laser cooling. By shining a red-detuned laser in the direction opposite to the motion of a particle, the particle can absorb a photon. This reduces the velocity of the particle due to momentum con- servation. Hereafter, the photon is emitted in an arbitrary direction and therefore on average the velocity of the particle is reduced. By using this principle, temperatures of the order of 10 µK are achievable. Since this is still not low enough for achieving BEC, laser cooling is followed by evapo- rative cooling. Evaporative cooling is a process where the most energetic particles are removed from the system. By simply reducing the height of the trapping potential, the particles with the highest energy escape. This process is illustrated in Fig. 1.1. This reduces the average temperatures of the gas to the nanokelvin regime, which was sufficient for the first observa- tion of BEC in atomic vapors [3{5]. There are several experiments that can be performed to distinguish whether a Bose gas is in the Bose-Einstein condensed phase or not. The most obvious experiment is measuring the density of particles and therefrom extracting the number of particles in the ground state. Another possibility 1.1. BOSE-EINSTEIN CONDENSATION OF ATOMS 13 is performing correlation measurements and in particular investigating the one-particle density matrix n(x; x0). In the language of second quantiza- tion, it is given by n(x; x0) = ^y(x) ^(x0) ; (1.2) h i where ^y(x) and ^(x0) are the creation and annihilation operator of the atoms. In an ordinary gas or liquid, the density matrix typically decays exponentially as a function of the separation x x . On the other hand, j − 0j for a macroscopic occupation of the ground state there is an additional contribution. Since this contribution is independent of the separation, we find that in the Bose-Einstein condensed phase the density matrix does not vanish at large separations. This so-called off-diagonal long-range order is another characteristic for BEC. True off-diagonal long-range order is only present in three dimensions. In lower dimensions, interaction effects will lead to fluctuations that affect the behavior of the single-particle density matrix. This is particularly im- portant in atomic vapors, since in these systems it is possible to manipulate the degrees of freedom of the particles. By changing the configuration of the external trapping potential, the motion of the atoms in one or two directions can be frozen out.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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].
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Introduction
    1 Introduction 1.1 Closed time contour Consider a quantum many-body system governed by a time-dependent Hamilto- nian H(t). Let us assume that in the distant past t the system was in a state ˆ =−∞ specified by a many-body density matrix ρ( ). The precise form of the latter is ˆ −∞ of no importance. It may be, e.g., the equilibrium density matrix associated with the Hamiltonian H( ). We shall also assume that the time-dependence of the ˆ −∞ Hamiltonian is such that at t the particles were non-interacting. The inter- =−∞ actions are then adiabatically switched on to reach their actual physical strength sometime prior to the observation time. In addition, the Hamiltonian may con- tain true time dependence through e.g. external fields or boundary conditions. Due to such true time-dependent perturbations the density matrix is driven away from equilibrium. The density matrix evolves according to the Von Neumann equation ∂t ρ(t) i H(t), ρ(t) , (1.1) ˆ =− ˆ ˆ where we set ! 1. It is formally solved! with the" help of the unitary evolution = † operator as ρ(t) t, ρ( ) t, t, ρ( ) ,t , where the † ˆ = Uˆ −∞ ˆ −∞ Uˆ −∞ = Uˆ −∞ ˆ −∞ Uˆ−∞ denotes Hermitian conjugation. The evolution operator obeys ! " ∂t t,t iH(t) t,t ∂t t,t i t,t H(t#). Uˆ # =− ˆ Uˆ # ; # Uˆ # = Uˆ # ˆ Notice that the Hamiltonian operators taken at different moments of time, in gen- eral, do not commute with each other. As a result, t,t must be understood as Uˆ # an infinite product of incremental evolution operators with instantaneous locally constant Hamiltonians iH(t δt )δt iH(t 2δt )δt iH(t Nδt )δt iH(t #)δt t,t lim e− ˆ − e− ˆ − ...e− ˆ − e− ˆ ˆ # = N U →∞ t T exp i H(t) dt , (1.2) = − ˆ # $t # % where an infinitesimal time-step is δt (t t#)/N and to shorten the notations the = − infinite product is abbreviated as the time-ordered, or T-exponent.
    [Show full text]
  • Classical and Quantum Out-Of-Equilibrium Dynamics
    Classical and quantum out-of-equilibrium dynamics. Formalism and applications. Camille Aron To cite this version: Camille Aron. Classical and quantum out-of-equilibrium dynamics. Formalism and applications.. Data Analysis, Statistics and Probability [physics.data-an]. Université Pierre et Marie Curie - Paris VI, 2010. English. tel-00538099 HAL Id: tel-00538099 https://tel.archives-ouvertes.fr/tel-00538099 Submitted on 21 Nov 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE` DE DOCTORAT DE L’UNIVERSITE´ PIERRE ET MARIE CURIE Specialit´ e´ : Physique theorique´ Ecole´ doctorale : ≪ La physique, de la particule au solide ≫ Realis´ ee´ au Laboratoire de Physique Theorique´ et Hautes Energies´ Present´ ee´ par M. Camille ARON Pour obtenir le grade de Docteur de l’Universite´ Pierre et Marie Curie Dynamique hors d’equilibre´ classique et quantique. Formalisme et applications. Soutenue le 20 septembre 2010 devant le jury compose´ de M. Denis BERNARD (President´ du jury) M. Federico CORBERI (Examinateur) me M Leticia CUGLIANDOLO (Directrice de these)` M. Gabriel KOTLIAR (Rapporteur) M. Marco PICCO (Invite)´ M. Fred´ eric´ Van WIJLAND (Rapporteur) A bracadabra. REMERCIEMENTS ES tous premiers vont bien naturellement a` ma directrice de these,` Leticia Cugliandolo.
    [Show full text]
  • Quantum Field Theory in Condensed Matter Physics
    QUANTUM FIELD THEORY IN CONDENSED MATTER PHYSICS Wolfgang Belzig FORMAL MATTERS “Wahlpflichtfach” 4h lecture + 2h exercise Lecture: Mon & Thu, 10-12, P603 Tutorial: Mon, 14-16 (P912) or 16-18 (P712) 50% of exercises needed for exam Language: “English” (German questions allowed) No lecture on 21. April, 25. April, 9. May, 2. June, 13. June, 16. June, 23. June, 14. July EXERCISE GROUPS • Two groups @ 14h (P912) and 16h (P712) • Distribution: see list • Exercise sheets usually 5-8 days before exercise (see webpage for preview) • Question on exercise to one of the tutors (preferably the one who is responsible) • Plan: 18.4. Milena Filipovic; 2.5. Martin Bruderer; 9.5. Fei Xu 16.5. Cecilia Holmqvist; 23.5. Peter Machon LITERATURE G. Rickayzen: Green’s functions and Condensed Matter H. Bruus and K. Flensberg: Many-Body Quantum Theory in Condensed Matter Physics J. Rammer: Quantum Field Theory of Non-equilibium States G. Mahan: Quantum Field Theoretical Methods Fetter & Walecka: Quantum Theory of Many Particle Systems Yu. V. Nazarov & Ya. Blanter: Quantum Transport J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986) CONTENT A. Introduction, the Problem B. Formalities, Definitions C. Diagrammatic Methods D. Disordered Conductors E. Electrons and Phonons F. Superconductivity G. Quasiclassical Methods H. Nonequilibrium and Keldysh formalism I. Quantum Transport and Quantum Noise PHYSICAL OVERVIEW Solid state physics: Many electrons and phonons interacting with the lattice potential and among each other (band structure, disorder, electron-electron
    [Show full text]
  • Quasiclassical Theory of Spin Dynamics in Superfluid $^ 3$ He
    Noname manuscript No. (will be inserted by the editor) Quasiclassical theory of spin dynamics in superfluid 3He: kinetic equations in the bulk and spin response of surface Majorana states M.A. Silaev Received: date / Accepted: date Abstract We develop a theory based on the formalism of quasiclassical Green’s functions to study the spin dynamics in superfluid 3He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid re- producing the results obtained earlier without quasiclassical approximation. Then we consider spin dynamics near the surface of fully gapped 3He-B phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetimes of longitudinal and transverse spin waves are cal- culated taking into account the Fermi-liquid corrections which lead to a crucial modification of fermionic spectrum and spin responses. Keywords Superfluid 3He Magnetic resonance Majorana states · · 1 Introduction The theory of spin dynamics in superfluid 3He has been developed for several decades since the pioneering works of Leggett [1,2,3], where the phenomenological equations were formulated explaining shifts of the transverse nuclear magnetic resonance mode and predicting longitudinal resonance in the B phase [4,5,6]. To study spin relaxation, that is the width of the NMR signal, Leggett and Takagi [7,8] introduced the two-fluid model which yields qualitatively the same results as the kinetic theory [9,10,11,12,13]. Nowadays, the most common approach to study non-equilibrium states in dif- ferent condensed matter systems including superconductors and Fermi superfluids is based on the quasiclassical Keldysh formalism.
    [Show full text]
  • Dicke Quantum Spin and Photon Glass in Optical Cavities: Non-Equilibrium Theory and Experimental Signatures
    Dicke Quantum Spin and Photon Glass in Optical Cavities: Non-equilibrium theory and experimental signatures Michael Buchhold,1 Philipp Strack,2 Subir Sachdev,2 and Sebastian Diehl1, 3 1Institut f¨urTheoretische Physik, Leopold-Franzens Universit¨atInnsbruck, A-6020 Innsbruck, Austria 2Department of Physics, Harvard University, Cambridge MA 02138 3Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interac- tions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter, and could evolve into a “cavity glass microscope” for frustrated quantum systems out-of-equilibrium. Here we develop the non-equilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class however is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, in- cluding the emergence of a common low-frequency effective temperature. The imprint of the atomic spin glass physics onto a “photon glass” makes it possible to detect the glass state by standard experimental techniques of quantum optics.
    [Show full text]
  • New Theoretical Approaches for Correlated Systems in Nonequilibrium
    Eur. Phys. J. Special Topics 180, 217–235 (2010) c EDP Sciences, Springer-Verlag 2010 THE EUROPEAN DOI: 10.1140/epjst/e2010-01219-x PHYSICAL JOURNAL SPECIAL TOPICS Review New theoretical approaches for correlated systems in nonequilibrium M. Eckstein1,A.Hackl2, S. Kehrein3, M. Kollar4,M.Moeckel5, P. Werner1, and F.A. Wolf4 1 Institute of Theoretical Physics, ETH Z¨urich, Wolfgang-Pauli-Str. 27, 8093 Z¨urich, Switzerland 2 Institute of Theoretical Physics, Universit¨atzu K¨oln,Z¨ulpicher Str. 77, 50937 K¨oln,Germany 3 Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Physics Department, Ludwig-Maximilians-Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany 4 Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, Universit¨at Augsburg, 86135 Augsburg, Germany 5 Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany Abstract. We review recent developments in the theory of interacting quan- tum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In non- equilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench.
    [Show full text]
  • Theory of Laser-Driven Nonequilibrium Superconducfvity Michael Sentef
    Theory of laser-driven nonequilibrium superconduc7vity PRB 92, 224517 (2015) Theory collaborators: A. F. Kemper, B. Moritz, J. K. Freericks, T. P. Devereaux, PRB 93, 144506 (2016) A. Georges, C. Kollath Michael Sentef New3SC Bled, September 14, 2016 Max Planck Institute for the Structure and Dynamics of Matter Pump-probe spectroscopy (1887) • stroboscopic inves7gaons of dynamic phenomena Muybridge 1887 Max Planck Institute for the Structure and Dynamics of Matter 2 Pump-probe spectroscopy (today) • stroboscopic inves7gaons of dynamic phenomena TbTe3 CDW metal J. Sobota et al., PRL 108, 117403 (2012) F. SchmiA et al., Science 321, 1649 (2008) Image courtesy: J. Sobota / F. SchmiA Max Planck Institute for the Structure and Dynamics of Matter 3 Ultrafast Materials Science Understanding the nature of QuasiparRcles § Relaxaon dynamics PRL 111, 077401 (2013) PRX 3, 041033 (2013) PRB 87, 235139 (2013) PRB 90, 075126 (2014) arXiv:1505.07055 arXiv:1607.02314 Understanding ordered phases § Collec7ve oscillaons § Compe7ng order parameters PRB 92, 224517 (2015) PRB 93, 144506 (2016) CreaRng new states of maAer § Photo-induced phase transi7ons § Floquet topological states Image courtesy: Nature Commun. 6, 7047 (2015) D. Basov arXiv:1604.03399 Max Planck Institute for the Structure and Dynamics of Matter 4 Outline • Keldysh Green funcons • Ordered states: Driven superconductors – Higgs amplitude mode oscillaons for op7cal pumping (1.5 eV laser) PRB 92, 224517 (2015) – light-enhanced superconduc7vity via hopping control PRB 93, 144506 (2016) Max Planck Institute for the Structure and Dynamics of Matter 5 2 been successfully used to describe the melting of a charge non-dispersive optical phonon with energy ⇥. As our density-wave state24 and the time evolution of electrons starting point, we use the Holstein model which couples in correlated metals25,26 via tr-ARPES and tr-reflectivity.
    [Show full text]