Fundamentals and New Frontiers of Bose Einstein Condensation

Size: px
Start display at page:

Download "Fundamentals and New Frontiers of Bose Einstein Condensation"

Transcription

1 Contents Preface v 1. Fundamentals of Bose Einstein Condensation Indistinguishability of Identical Particles Ideal Bose Gas in a Uniform System Off-Diagonal Long-Range Order: Bose System Off-Diagonal Long-Range Order: Fermi System U(1) Gauge Symmetry Ground-State Wave Function of a Bose System BECandSuperfluidity Two-Fluid Model Fragmented Condensate Two-state model Degenerate double-well model Spin-1 antiferromagnetic BEC Interference Between Independent Condensates FeshbachResonance Weakly Interacting Bose Gas Interactions Between Neutral Atoms Pseudo-PotentialMethod Bogoliubov Theory Bogoliubov transformations Bogoliubov ground state Low-lying excitations and condensate fraction Properties of Bogoliubov ground state xi

2 xii Fundamentals and New Frontiers of Bose Einstein Condensation 2.4 Bogoliubov Theory of Quasi-One-Dimensional Torus Case of BEC at rest: stability of BEC Case of rotating BEC: Landau criterion Ground state of BEC in rotating torus Bogoliubov de Gennes (BdG) Theory Method of Binary Collision Expansion Equationofstate Cluster expansion of partition function Ideal Bose and Fermi gases Matsubaraformula Trapped Systems Ideal Bose Gas in a Harmonic Potential Transition temperature Condensate fraction Chemical potential Specific heat BEC in One- and Two-Dimensional Parabolic Potentials Density of states Transition temperature Condensate fraction Semiclassical Distribution Function Gross Pitaevskii Equation Thomas FermiApproximation Collective Modes in the Thomas Fermi Regime Isotropic harmonic potential Axisymmetric trap Scissorsmode VariationalMethod Gaussian variational wave function Collective modes Attractive Bose Einstein Condensate Collective modes Collapsing dynamics of an attractive condensate Linear Response and Sum Rules Linear Response Theory Linear response of density fluctuations

3 Contents xiii Retarded response function Sum Rules Longitudinal f-sum rule Compressibility sum rule Zero energy gap theorem Josephson sum rule Sum-Rule Approach to Collective Modes Excitation operators Virial theorem Kohntheorem Isotropictrap Axisymmetric trap Statistical Mechanics of Superfluid Systems in a Moving Frame Transformation to Moving Frames Elementary Excitations of a Superfluid Landau Criterion Correlation Functions at Thermal Equilibrium Normal Fluid Density Low-Lying Excitations of a Superfluid Examples Ideal Bose gas Weakly interacting Bose gas Spinor Bose Einstein Condensate Internal Degrees of Freedom General Hamiltonian of Spinor Condensates Spin-1 BEC Mean-field theory of a spin-1 BEC Many-body states in single-mode approximation Superflow, spin texture, and Berry phase Spin-2 BEC Vortices Hydrodynamic Theory of Vortices Quantized Vortices Interaction Between Vortices VortexLattice

4 xiv Fundamentals and New Frontiers of Bose Einstein Condensation Dynamics of vortex nucleation Collective modes of a vortex lattice Fractional Vortices Spin Current Fast Rotating BECs Lowest Landau level approximation Mean field quantum Hall regime Many-body wave functions of a fast rotating BEC Fermionic Superfluidity Ideal Fermi Gas Fermi Liquid Theory Cooper Problem Two-body problem Many-body problem Bardeen Cooper Schrieffer (BCS) Theory BCS BEC Crossover at T = Superfluid Transition Temperature BCS BEC Crossover at T Gor kov Melik Barkhudarov Correction Unitary Gas Imbalanced Fermi Systems P-Wave Superfluid Generalized pairing theory Spin-triplet p-wavestates Low-Dimensional Systems Non-interacting Systems Hohenberg Mermin Wagner Theorem Two-Dimensional BEC at Absolute Zero Berezinskii Kosterlitz Thouless Transition Universaljump Quasi long-range order Renormalization-group analysis Quasi One-Dimensional BEC Tonks Girardeau Gas Lieb Liniger Model

5 Contents xv 10. Dipolar Gases Dipole Dipole Interaction Basic properties Order of magnitude and length scale D-wave nature Tuning the dipole dipole interaction Polarized Dipolar BEC Nonlocal Gross Pitaevskii equation Stability Thomas Fermi limit Quasi two-dimensional systems Spinor-Dipolar BEC Einstein de Haas effect Flux closure and ground-state circulation Optical Lattices Optical Potential Optical trap Optical lattice Band Structure Bloch theorem Brillouin zone Bloch oscillations Wannier function Bose Hubbard Model Bose Hubbard Hamiltonian Superfluid Mott-insulator transition Phase diagram Mean-field approximation Supersolid Topological Excitations Homotopy Theory Homotopic relation Fundamental group Higher homotopy groups Order Parameter Manifold Isotropy group

6 xvi Fundamentals and New Frontiers of Bose Einstein Condensation Spin-1 BEC Spin-2 BEC Classification of Defects Domains Linedefects Point defects Skyrmions Influence of different types of defects Topological charges Appendix A Order of Phase Transition, Clausius Clapeyron Formula, and Gibbs Duhem Relation 321 Appendix B Bogoliubov Wave Functions in Coordinate Space 323 B.1 Ground-State Wave Function B.2 One-Phonon State Appendix C Effective Mass, Sound Velocity, and Spin Susceptibility of Fermi Liquid 329 Appendix D Derivation of Eq. (8.155) 333 Appendix E f - Sum Rule 335 Bibliography 337 Index 347

The Superfluid Phase s of Helium 3

The Superfluid Phase s of Helium 3 The Superfluid Phase s of Helium 3 DIETER VOLLHARD T Rheinisch-Westfälische Technische Hochschule Aachen, Federal Republic of German y PETER WÖLFL E Universität Karlsruhe Federal Republic of Germany PREFACE

More information

Ultra-cold gases. Alessio Recati. CNR INFM BEC Center/ Dip. Fisica, Univ. di Trento (I) & Dep. Physik, TUM (D) TRENTO

Ultra-cold gases. Alessio Recati. CNR INFM BEC Center/ Dip. Fisica, Univ. di Trento (I) & Dep. Physik, TUM (D) TRENTO Ultra-cold gases Alessio Recati CNR INFM BEC Center/ Dip. Fisica, Univ. di Trento (I) & Dep. Physik, TUM (D) TRENTO Lectures L. 1) Introduction to ultracold gases Bosonic atoms: - From weak to strong interacting

More information

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9 Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................

More information

Contents Preface Physical Constants, Units, Mathematical Signs and Symbols Introduction Kinetic Theory and the Boltzmann Equation

Contents Preface Physical Constants, Units, Mathematical Signs and Symbols Introduction Kinetic Theory and the Boltzmann Equation V Contents Preface XI Physical Constants, Units, Mathematical Signs and Symbols 1 Introduction 1 1.1 Carbon Nanotubes 1 1.2 Theoretical Background 4 1.2.1 Metals and Conduction Electrons 4 1.2.2 Quantum

More information

Fundamentals and New Frontiers of Bose Einstein Condensation

Fundamentals and New Frontiers of Bose Einstein Condensation Experimental realization of Bose Einstein condensation (BEC) of dilute atomic gases [Anderson, et al. (1995); Davis, et al. (1995); Bradley, et al. (1995, 1997)] has ignited a virtual explosion of research.

More information

SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES

SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES College de France, May 14, 2013 SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES Sandro Stringari Università di Trento CNR-INFM PLAN OF THE LECTURES Lecture 1. Superfluidity in ultra cold atomic gases: examples

More information

Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007

Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007 1859-5 Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases 27 August - 7 September, 2007 Dipolar BECs with spin degrees of freedom Yuki Kawaguchi Tokyo Institute of

More information

Preface Introduction to the electron liquid

Preface Introduction to the electron liquid Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2

More information

From BEC to BCS. Molecular BECs and Fermionic Condensates of Cooper Pairs. Preseminar Extreme Matter Institute EMMI. and

From BEC to BCS. Molecular BECs and Fermionic Condensates of Cooper Pairs. Preseminar Extreme Matter Institute EMMI. and From BEC to BCS Molecular BECs and Fermionic Condensates of Cooper Pairs Preseminar Extreme Matter Institute EMMI Andre Wenz Max-Planck-Institute for Nuclear Physics and Matthias Kronenwett Institute for

More information

Statistical Mechanics

Statistical Mechanics Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2

More information

Landau Theory of Fermi Liquids : Equilibrium Properties

Landau Theory of Fermi Liquids : Equilibrium Properties Quantum Liquids LECTURE I-II Landau Theory of Fermi Liquids : Phenomenology and Microscopic Foundations LECTURE III Superfluidity. Bogoliubov theory. Bose-Einstein condensation. LECTURE IV Luttinger Liquids.

More information

Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and

More information

Low dimensional quantum gases, rotation and vortices

Low dimensional quantum gases, rotation and vortices Goal of these lectures Low dimensional quantum gases, rotation and vortices Discuss some aspect of the physics of quantum low dimensional systems Planar fluids Quantum wells and MOS structures High T c

More information

SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester

SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester SOLID STATE PHYSICS Second Edition J. R. Hook H. E. Hall Department of Physics, University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE Contents Flow diagram Inside front

More information

Non-Equilibrium Physics with Quantum Gases

Non-Equilibrium Physics with Quantum Gases Non-Equilibrium Physics with Quantum Gases David Weiss Yang Wang Laura Adams Cheng Tang Lin Xia Aishwarya Kumar Josh Wilson Teng Zhang Tsung-Yao Wu Neel Malvania NSF, ARO, DARPA, Outline Intro: cold atoms

More information

Vortices and other topological defects in ultracold atomic gases

Vortices and other topological defects in ultracold atomic gases Vortices and other topological defects in ultracold atomic gases Michikazu Kobayashi (Kyoto Univ.) 1. Introduction of topological defects in ultracold atoms 2. Kosterlitz-Thouless transition in spinor

More information

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific

More information

Design and realization of exotic quantum phases in atomic gases

Design and realization of exotic quantum phases in atomic gases Design and realization of exotic quantum phases in atomic gases H.P. Büchler and P. Zoller Theoretische Physik, Universität Innsbruck, Austria Institut für Quantenoptik und Quanteninformation der Österreichischen

More information

Introduction to Cold Atoms and Bose-Einstein Condensation. Randy Hulet

Introduction to Cold Atoms and Bose-Einstein Condensation. Randy Hulet Introduction to Cold Atoms and Bose-Einstein Condensation Randy Hulet Outline Introduction to methods and concepts of cold atom physics Interactions Feshbach resonances Quantum Gases Quantum regime nλ

More information

Spinor Bose gases lecture outline

Spinor Bose gases lecture outline Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor Bose-Einstein condensates 3. Imaging spin textures 4. Spin-mixing dynamics 5. Magnetic excitations We re here Coupling

More information

SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES

SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES Congresso Nazionale della Società Italiana di Fisica Università della Calabria 17/21 Settembre 2018 SYNTHETIC GAUGE FIELDS IN ULTRACOLD ATOMIC GASES Sandro Stringari Università di Trento CNR-INO - Bose-Einstein

More information

On the Higgs mechanism in the theory of

On the Higgs mechanism in the theory of On the Higgs mechanism in the theory of superconductivity* ty Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften D-85748 Garching Outline Phenomenological

More information

Strongly correlated Cooper pair insulators and superfluids

Strongly correlated Cooper pair insulators and superfluids Strongly correlated Cooper pair insulators and superfluids Predrag Nikolić George Mason University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Affiliations and

More information

Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC FERMI GASES

Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC FERMI GASES 1 INTERNATIONAL SCHOOL OF PHYSICS "ENRICO FERMI" Varenna, July 1st - July 11 th 2008 " QUANTUM COHERENCE IN SOLID STATE SYSTEMS " Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC

More information

Spontaneous Symmetry Breaking in Bose-Einstein Condensates

Spontaneous Symmetry Breaking in Bose-Einstein Condensates The 10th US-Japan Joint Seminar Spontaneous Symmetry Breaking in Bose-Einstein Condensates Masahito UEDA Tokyo Institute of Technology, ERATO, JST collaborators Yuki Kawaguchi (Tokyo Institute of Technology)

More information

List of Comprehensive Exams Topics

List of Comprehensive Exams Topics List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle

More information

Field Theories in Condensed Matter Physics. Edited by. Sumathi Rao. Harish-Chandra Research Institute Allahabad. lop

Field Theories in Condensed Matter Physics. Edited by. Sumathi Rao. Harish-Chandra Research Institute Allahabad. lop Field Theories in Condensed Matter Physics Edited by Sumathi Rao Harish-Chandra Research Institute Allahabad lop Institute of Physics Publishing Bristol and Philadelphia Contents Preface xiii Introduction

More information

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I)

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) B.V. COSTA UFMG BRAZIL LABORATORY FOR SIMULATION IN PHYSICS A Guide to Monte Carlo Simulations in Statistical Physics by Landau

More information

Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007

Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007 Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007 L.P. Pitaevskii Dipartimento di Fisica, Universita di Trento, INFM BEC CNR,Trento, Italy; Kapitza Institute for Physical Problems, ul.

More information

The BCS-BEC Crossover and the Unitary Fermi Gas

The BCS-BEC Crossover and the Unitary Fermi Gas Lecture Notes in Physics 836 The BCS-BEC Crossover and the Unitary Fermi Gas Bearbeitet von Wilhelm Zwerger 1. Auflage 2011. Taschenbuch. xvi, 532 S. Paperback ISBN 978 3 642 21977 1 Format (B x L): 15,5

More information

Harvard University Physics 284 Spring 2018 Strongly correlated systems in atomic and condensed matter physics

Harvard University Physics 284 Spring 2018 Strongly correlated systems in atomic and condensed matter physics 1 Harvard University Physics 284 Spring 2018 Strongly correlated systems in atomic and condensed matter physics Instructor Eugene Demler Office: Lyman 322 Email: demler@physics.harvard.edu Teaching Fellow

More information

INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition

INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa

More information

Strongly Correlated Physics With Ultra-Cold Atoms

Strongly Correlated Physics With Ultra-Cold Atoms Strongly Correlated Physics With Ultra-Cold Atoms Predrag Nikolić Rice University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Sponsors W.M.Keck Program in Quantum

More information

Interaction between atoms

Interaction between atoms Interaction between atoms MICHA SCHILLING HAUPTSEMINAR: PHYSIK DER KALTEN GASE INSTITUT FÜR THEORETISCHE PHYSIK III UNIVERSITÄT STUTTGART 23.04.2013 Outline 2 Scattering theory slow particles / s-wave

More information

Superfluidity of a 2D Bose gas (arxiv: v1)

Superfluidity of a 2D Bose gas (arxiv: v1) Superfluidity of a 2D Bose gas (arxiv:1205.4536v1) Christof Weitenberg, Rémi Desbuquois, Lauriane Chomaz, Tarik Yefsah, Julian Leonard, Jérôme Beugnon, Jean Dalibard Trieste 18.07.2012 Phase transitions

More information

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields

More information

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and :

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and : Wednesday, April 23, 2014 9:37 PM Excitations in a Bose condensate So far: basic understanding of the ground state wavefunction for a Bose-Einstein condensate; We need to know: elementary excitations in

More information

Quantum Theory of Matter

Quantum Theory of Matter Quantum Theory of Matter Revision Lecture Derek Lee Imperial College London May 2006 Outline 1 Exam and Revision 2 Quantum Theory of Matter Microscopic theory 3 Summary Outline 1 Exam and Revision 2 Quantum

More information

(1) BEC (2) BEC (1) (BEC) BEC BEC (5) BEC (LT) (QFS) BEC (3) BEC. 3 He. 4 He. 4 He 3 He

(1) BEC (2) BEC (1) (BEC) BEC BEC (5) BEC (LT) (QFS) BEC (3) BEC. 3 He. 4 He. 4 He 3 He 22 (BEC) 4 He BEC We study theoretically and experimentally quantum hydrodynamics in quantum condensed phases at low temperature, namely superfluid helium and atomic Bose-Einstein condensates (BECs). Quantum

More information

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Content-Thermodynamics & Statistical Mechanics 1. Kinetic theory of gases..(1-13) 1.1 Basic assumption of kinetic theory 1.1.1 Pressure exerted by a gas 1.2 Gas Law for Ideal gases: 1.2.1 Boyle s Law 1.2.2

More information

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke BCS-BEC Crossover Hauptseminar: Physik der kalten Gase Robin Wanke Outline Motivation Cold fermions BCS-Theory Gap equation Feshbach resonance Pairing BEC of molecules BCS-BEC-crossover Conclusion 2 Motivation

More information

5. Gross-Pitaevskii theory

5. Gross-Pitaevskii theory 5. Gross-Pitaevskii theory Outline N noninteracting bosons N interacting bosons, many-body Hamiltonien Mean-field approximation, order parameter Gross-Pitaevskii equation Collapse for attractive interaction

More information

April Schafroth s bosons? 2. BCS paired electrons? 3. Lattice Bosons?! -- new paradigm of metallic conductivity

April Schafroth s bosons? 2. BCS paired electrons? 3. Lattice Bosons?! -- new paradigm of metallic conductivity April 2011 1. Schafroth s bosons? 2. BCS paired electrons? 3. Lattice Bosons?! -- new paradigm of metallic conductivity Energy transport solar cells nuclear energy wind energy 15% of electric power is

More information

Many-Body Anderson Localization in Disordered Bose Gases

Many-Body Anderson Localization in Disordered Bose Gases Many-Body Anderson Localization in Disordered Bose Gases Laurent Sanchez-Palencia Laboratoire Charles Fabry - UMR8501 Institut d'optique, CNRS, Univ. Paris-sud 11 2 av. Augustin Fresnel, Palaiseau, France

More information

Principles of Condensed matter physics

Principles of Condensed matter physics Principles of Condensed matter physics P. M. CHAIKIN Princeton University T. C. LUBENSKY University of Pennsylvania CAMBRIDGE UNIVERSITY PRESS Preface xvii 1 Overview 1 1.1 Condensed matter physics 1 1.2

More information

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles October, 011 PROGRESS IN PHYSICS olume 4 Ultracold Fermi Bose Gases Spinless Bose Charged Sound Particles ahan N. Minasyan alentin N. Samoylov Scientific Center of Applied Research, JINR, Dubna, 141980,

More information

Solid State Physics. GIUSEPPE GROSSO Professor of Solid State Physics, Department of Physics, University of Pavia, and INFM

Solid State Physics. GIUSEPPE GROSSO Professor of Solid State Physics, Department of Physics, University of Pavia, and INFM Solid State Physics GIUSEPPE GROSSO Professor of Solid State Physics, Department of Physics, University of Pisa, and INFM GIUSEPPE PASTORI PARRAVICINI Professor of Solid State Physics, Department of Physics,

More information

Superfluidity. v s. E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN University of Oulu, Finland (Dated: June 8, 2012)

Superfluidity. v s. E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN University of Oulu, Finland (Dated: June 8, 2012) Superfluidity E. V. Thuneberg Department of Physical Sciences, P.O.Box 3000, FIN-90014 University of Oulu, Finland (Dated: June 8, 01) PACS numbers: 67.40.-w, 67.57.-z, 74., 03.75.-b I. INTRODUCTION Fluids

More information

When superfluids are a drag

When superfluids are a drag When superfluids are a drag KITP October 2008 David Roberts Los Alamos National Laboratory In collaboration with Yves Pomeau (ENS), Andrew Sykes (Queensland), Matt Davis (Queensland), What makes superfluids

More information

ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs

ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs INT Seattle 5 March 5 ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs Yun Li, Giovanni Martone, Lev Pitaevskii and Sandro Stringari University of Trento CNR-INO Now in Swinburne Now in Bari Stimulating discussions

More information

Lecture 4: Superfluidity

Lecture 4: Superfluidity Lecture 4: Superfluidity Previous lecture: Elementary excitations above condensate are phonons in the low energy limit. This lecture Rotation of superfluid helium. Hess-Fairbank effect and persistent currents

More information

Effects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in 2D Fermi Gases

Effects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in 2D Fermi Gases Effects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in D Fermi Gases Carlos A. R. Sa de Melo Georgia Institute of Technology QMath13 Mathematical Results in Quantum

More information

The Mott Metal-Insulator Transition

The Mott Metal-Insulator Transition Florian Gebhard The Mott Metal-Insulator Transition Models and Methods With 38 Figures Springer 1. Metal Insulator Transitions 1 1.1 Classification of Metals and Insulators 2 1.1.1 Definition of Metal

More information

Confining ultracold atoms on a ring in reduced dimensions

Confining ultracold atoms on a ring in reduced dimensions Confining ultracold atoms on a ring in reduced dimensions Hélène Perrin Laboratoire de physique des lasers, CNRS-Université Paris Nord Charge and heat dynamics in nano-systems Orsay, October 11, 2011 What

More information

Quantum fluid phenomena with Microcavity Polaritons. Alberto Bramati

Quantum fluid phenomena with Microcavity Polaritons. Alberto Bramati Quantum fluid phenomena with Microcavity Polaritons Alberto Bramati Quantum Optics Team: topics Quantum fluid phenomena in polariton gases An ideal system to study out of equilibrium quantum fluids Obstacle

More information

A Mixture of Bose and Fermi Superfluids. C. Salomon

A Mixture of Bose and Fermi Superfluids. C. Salomon A Mixture of Bose and Fermi Superfluids C. Salomon Enrico Fermi School Quantum Matter at Ultralow Temperatures Varenna, July 8, 2014 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner, C.S. Lithium

More information

Contents. Appendix A Strong limit and weak limit 35. Appendix B Glauber coherent states 37. Appendix C Generalized coherent states 41

Contents. Appendix A Strong limit and weak limit 35. Appendix B Glauber coherent states 37. Appendix C Generalized coherent states 41 Contents Preface 1. The structure of the space of the physical states 1 1.1 Introduction......................... 1 1.2 The space of the states of physical particles........ 2 1.3 The Weyl Heisenberg algebra

More information

The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other

The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other 1 The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other phases of matter that have been experimentally observed,

More information

Superfluid Helium 3 Topological Defects as a Consequence of Broken Symmetry. Matthias Brasse. December 11, 2007

Superfluid Helium 3 Topological Defects as a Consequence of Broken Symmetry. Matthias Brasse. December 11, 2007 Superfluid Helium 3 Topological Defects as a Consequence of Broken Symmetry Matthias Brasse December 11, 2007 Abstract Superfluid phases in helium 3 were firstly discovered in 1972. They arise from the

More information

The Oxford Solid State Basics

The Oxford Solid State Basics The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed

More information

Statistical Mechanics

Statistical Mechanics Statistical Mechanics Entropy, Order Parameters, and Complexity James P. Sethna Laboratory of Atomic and Solid State Physics Cornell University, Ithaca, NY OXFORD UNIVERSITY PRESS Contents List of figures

More information

Superfluidity and Condensation

Superfluidity and Condensation Christian Veit 4th of June, 2013 2 / 29 The discovery of superfluidity Early 1930 s: Peculiar things happen in 4 He below the λ-temperature T λ = 2.17 K 1938: Kapitza, Allen & Misener measure resistance

More information

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases Bahram M. Askerov Sophia R. Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases With im Figures Springer Contents 1 Basic Concepts of Thermodynamics and Statistical Physics...

More information

From laser cooling to BEC First experiments of superfluid hydrodynamics

From laser cooling to BEC First experiments of superfluid hydrodynamics From laser cooling to BEC First experiments of superfluid hydrodynamics Alice Sinatra Quantum Fluids course - Complement 1 2013-2014 Plan 1 COOLING AND TRAPPING 2 CONDENSATION 3 NON-LINEAR PHYSICS AND

More information

A Mixture of Bose and Fermi Superfluids. C. Salomon

A Mixture of Bose and Fermi Superfluids. C. Salomon A Mixture of Bose and Fermi Superfluids C. Salomon INT workshop Frontiers in quantum simulation with cold atoms University of Washington, April 2, 2015 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner,

More information

Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases

Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases Michael KöhlK ETH Zürich Z (www.quantumoptics.ethz.ch( www.quantumoptics.ethz.ch) Introduction Why should a condensed matter physicist

More information

Cold atoms. 1: Bose-Einstein Condensation. Emil Lundh. April 13, Department of Physics Umeå University

Cold atoms. 1: Bose-Einstein Condensation. Emil Lundh. April 13, Department of Physics Umeå University 1: Bose-Einstein Condensation Department of Physics Umeå University lundh@tp.umu.se April 13, 2011 Umeå 114 000 inhabitants Average age 37.9 years Cultural capital of Europe 2014 400 km ski tracks 180

More information

FERMI-HUBBARD PHYSICS WITH ATOMS IN AN OPTICAL LATTICE 1

FERMI-HUBBARD PHYSICS WITH ATOMS IN AN OPTICAL LATTICE 1 FERMI-HUBBARD PHYSICS WITH ATOMS IN AN OPTICAL LATTICE 1 Tilman Esslinger, Department of Physics, ETH Zurich, Switzerland ABSTRACT The Fermi-Hubbard model is a key concept in condensed matter physics and

More information

Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1

Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1 xi Contents Preface Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii viii ix 1 Introduction 1 I GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5 Diverse limited approaches:

More information

Equation of state of the unitary Fermi gas

Equation of state of the unitary Fermi gas Equation of state of the unitary Fermi gas Igor Boettcher Institute for Theoretical Physics, University of Heidelberg with S. Diehl, J. M. Pawlowski, and C. Wetterich C o ld atom s Δ13, 11. 1. 2013 tio

More information

5 Topological defects and textures in ordered media

5 Topological defects and textures in ordered media 5 Topological defects and textures in ordered media In this chapter we consider how to classify topological defects and textures in ordered media. We give here only a very short account of the method following

More information

Theory Seminar Uni Marburg. Bose-Einstein Condensation and correlations in magnon systems

Theory Seminar Uni Marburg. Bose-Einstein Condensation and correlations in magnon systems Theory Seminar Uni Marburg 11 November, 2010 Bose-Einstein Condensation and correlations in magnon systems Peter Kopietz, Universität Frankfurt 1.) Bose-Einstein condensation 2.) Interacting magnons in

More information

Quantum Theory of Matter

Quantum Theory of Matter Quantum Theory of Matter Overview Lecture Derek Lee Imperial College London January 2007 Outline 1 Course content Introduction Superfluids Superconductors 2 Course Plan Resources Outline 1 Course content

More information

Exchange statistics. Basic concepts. University of Oxford April, Jon Magne Leinaas Department of Physics University of Oslo

Exchange statistics. Basic concepts. University of Oxford April, Jon Magne Leinaas Department of Physics University of Oslo University of Oxford 12-15 April, 2016 Exchange statistics Basic concepts Jon Magne Leinaas Department of Physics University of Oslo Outline * configuration space with identifications * from permutations

More information

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer Franz Schwabl QUANTUM MECHANICS Translated by Ronald Kates Second Revised Edition With 122Figures, 16Tables, Numerous Worked Examples, and 126 Problems ff Springer Contents 1. Historical and Experimental

More information

Harald Ibach Hans Lüth SOLID-STATE PHYSICS. An Introduction to Theory and Experiment

Harald Ibach Hans Lüth SOLID-STATE PHYSICS. An Introduction to Theory and Experiment Harald Ibach Hans Lüth SOLID-STATE PHYSICS An Introduction to Theory and Experiment With 230 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents

More information

Quasi Two-Dimensional 6 Li Fermi gas

Quasi Two-Dimensional 6 Li Fermi gas Quasi Two-Dimensional 6 Li Fermi gas A thesis submitted for the degree of Doctor of Philosophy by Paul Dyke Centre for Atom Optics and Ultrafast Spectroscopy and ARC Centre of Excellence for Quantum-Atom

More information

1 Superfluidity and Bose Einstein Condensate

1 Superfluidity and Bose Einstein Condensate Physics 223b Lecture 4 Caltech, 04/11/18 1 Superfluidity and Bose Einstein Condensate 1.6 Superfluid phase: topological defect Besides such smooth gapless excitations, superfluid can also support a very

More information

Cold Atomic Gases. California Condensed Matter Theory Meeting UC Riverside November 2, 2008

Cold Atomic Gases. California Condensed Matter Theory Meeting UC Riverside November 2, 2008 New Physics with Interacting Cold Atomic Gases California Condensed Matter Theory Meeting UC Riverside November 2, 2008 Ryan Barnett Caltech Collaborators: H.P. Buchler, E. Chen, E. Demler, J. Moore, S.

More information

Quantum Fluids and Solids. Christian Enss (4He) & Henri Godfrin (3He)

Quantum Fluids and Solids. Christian Enss (4He) & Henri Godfrin (3He) Quantum Fluids and Solids Christian Enss (4He) & Henri Godfrin (3He) What Do We Consider as Quantum Matter? φ Lennard Jones Potential σ ε r De Boer quantum parameter: De Broglie wavelength: Introduction

More information

Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas

Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas / 6 Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas Giovanni Italo Martone with G. V. Shlyapnikov Worhshop on Exploring Nuclear Physics with Ultracold Atoms

More information

Vortex States in a Non-Abelian Magnetic Field

Vortex States in a Non-Abelian Magnetic Field Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM

More information

Collective Effects. Equilibrium and Nonequilibrium Physics

Collective Effects. Equilibrium and Nonequilibrium Physics Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 3, 3 March 2006 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech

More information

Multi-Body Interacting Bosons. Dmitry Petrov Laboratoire Physique Théorique et Modèles Statistiques (Orsay)

Multi-Body Interacting Bosons. Dmitry Petrov Laboratoire Physique Théorique et Modèles Statistiques (Orsay) Multi-Body Interacting Bosons Dmitry Petrov Laboratoire Physique Théorique et Modèles Statistiques (Orsay) Outline Effective multi-body interactions Multi-body interacting systems. Why interesting? How

More information

Vortices and vortex states of Rashba spin-orbit coupled condensates

Vortices and vortex states of Rashba spin-orbit coupled condensates Vortices and vortex states of Rashba spin-orbit coupled condensates Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University March 5, 2014 P.N, T.Duric, Z.Tesanovic,

More information

Lecture 3 : ultracold Fermi Gases

Lecture 3 : ultracold Fermi Gases Lecture 3 : ultracold Fermi Gases The ideal Fermi gas: a reminder Interacting Fermions BCS theory in a nutshell The BCS-BEC crossover and quantum simulation Many-Body Physics with Cold Gases Diluteness:

More information

Superfluid Helium-3: From very low Temperatures to the Big Bang

Superfluid Helium-3: From very low Temperatures to the Big Bang Superfluid Helium-3: From very low Temperatures to the Big Bang Universität Frankfurt; May 30, 2007 Dieter Vollhardt Contents: The quantum liquids 3 He and 4 He Superfluid phases of 3 He Broken symmetries

More information

Lecture 2: Weak Interactions and BEC

Lecture 2: Weak Interactions and BEC Lecture 2: Weak Interactions and BEC Previous lecture: Ideal gas model gives a fair intuition for occurrence of BEC but is unphysical (infinite compressibility, shape of condensate...) Order parameter

More information

Magnetism in Condensed Matter

Magnetism in Condensed Matter Magnetism in Condensed Matter STEPHEN BLUNDELL Department of Physics University of Oxford OXFORD 'UNIVERSITY PRESS Contents 1 Introduction 1.1 Magnetic moments 1 1 1.1.1 Magnetic moments and angular momentum

More information

PHASE TRANSITIONS AND CRITICAL PHENOMENA

PHASE TRANSITIONS AND CRITICAL PHENOMENA INTRODUCTION TO PHASE TRANSITIONS AND CRITICAL PHENOMENA BY H. EUGENE STANLEY Boston University OXFORD UNIVERSITY PRESS New York Oxford CONTENTS NOTATION GUIDE xv PART I INTRODUCTION 1. WHAT ARE THE CRITICAL

More information

Superfluidity. Krzysztof Myśliwy. October 30, Theoretical Physics Proseminar

Superfluidity. Krzysztof Myśliwy. October 30, Theoretical Physics Proseminar Superfluidity Krzysztof Myśliwy Theoretical Physics Proseminar October 30, 2017 Outline The λ transition Phenomenology of He-II Landau theory- a semi-phenomenological approach Feynman s explanation- from

More information

Quantum critical itinerant ferromagnetism

Quantum critical itinerant ferromagnetism Quantum critical itinerant ferromagnetism Belitz et al., PRL 2005 Gareth Conduit Cavendish Laboratory University of Cambridge Two types of ferromagnetism Localized ferromagnetism: moments localised in

More information

Michikazu Kobayashi. Kyoto University

Michikazu Kobayashi. Kyoto University Topological Excitations and Dynamical Behavior in Bose-Einstein Condensates and Other Systems Michikazu Kobayashi Kyoto University Oct. 24th, 2013 in Okinawa International Workshop for Young Researchers

More information

Loop current order in optical lattices

Loop current order in optical lattices JQI Summer School June 13, 2014 Loop current order in optical lattices Xiaopeng Li JQI/CMTC Outline Ultracold atoms confined in optical lattices 1. Why we care about lattice? 2. Band structures and Berry

More information

Steven W. Van Sciver. Helium Cryogenics. Second Edition. 4) Springer

Steven W. Van Sciver. Helium Cryogenics. Second Edition. 4) Springer Steven W. Van Sciver Helium Cryogenics Second Edition 4) Springer Contents 1 Cryogenic Principles and Applications 1 1.1 Temperature Scale 2 1.2 Historical Background 4 1.3 Applications for Cryogenics

More information

Roton Mode in Dipolar Bose-Einstein Condensates

Roton Mode in Dipolar Bose-Einstein Condensates Roton Mode in Dipolar Bose-Einstein Condensates Sandeep Indian Institute of Science Department of Physics, Bangalore March 14, 2013 BECs vs Dipolar Bose-Einstein Condensates Although quantum gases are

More information

Reference for most of this talk:

Reference for most of this talk: Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding ultracold Fermi gases. in Ultracold Fermi Gases, Proceedings of the International School

More information

Microcavity Exciton-Polariton

Microcavity Exciton-Polariton Microcavity Exciton-Polariton Neil Na ( 那允中 ) Institute of Photonics Technologies National Tsing-Hua University 5/3/2012 Outline Microcavity Exciton-polariton QW excitons Microcavity photons Strong coupling

More information

Non-equilibrium phenomena in spinor Bose gases. Dan Stamper-Kurn University of California, Berkeley

Non-equilibrium phenomena in spinor Bose gases. Dan Stamper-Kurn University of California, Berkeley Non-equilibrium phenomena in spinor Bose gases Dan Stamper-Kurn University of California, Berkeley outline Introductory material Interactions under rotational symmetry Energy scales Ground states Spin

More information

Shigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA

Shigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA Shigeji Fujita and Salvador V Godoy Mathematical Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII Table of Contents and Categories XV Constants, Signs, Symbols, and General Remarks

More information