The BCS-BEC Crossover and the Unitary Fermi Gas

Transcription

1 Lecture Notes in Physics 836 The BCS-BEC Crossover and the Unitary Fermi Gas Bearbeitet von Wilhelm Zwerger 1. Auflage Taschenbuch. xvi, 532 S. Paperback ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 818 g Weitere Fachgebiete > Physik, Astronomie > Elektrodynakmik, Optik > Halbleiter- und Supraleiterphysik Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents 1 The BCS BEC Crossover and the Unitary Fermi Gas Introduction Feshbach Resonance Universality and Scale Invariance Thermodynamics and Critical Temperature Universal Tan Relations The Unitary Fermi Gas as a Perfect Fluid? RF Spectroscopy: Pairing Gap and Pseudogap Spin Imbalance and the Fermi Polaron FFLO Phases and Outlook References The BEC BCS Crossover: Some History and Some General Observations Introduction Some Prehistory Some General Remarks on the Crossover Problem References Crossovers in Unitary Fermi Systems Introduction and the Bertsch Problem Universality and Crossover Universality in the Unitarity Limit Thermodynamic Crossover Functions Finite Temperature Jastrow-Slater Approximation Short Range Correlations Instability in Multicomponent Systems Repulsive Interactions and Itinerant Ferromagnetism vii

3 viii Contents 3.3 Pairing in Uniform Systems and the BCS BEC Crossover BCS Limit Induced Interactions Leggett s BCS BEC Crossover NSR Atomic Traps and Nuclei Scaling in Atomic Traps Collective Modes Shell Structure and Pairing in Atomic Traps Pairing in Nuclei Quark and Gluon Matter Optical Lattices On-Site Attraction and Pairing On-Site Repulsion High Temperature Superconductivity in Optical Lattices Summary and Outlook References Pairing Fluctuations Approach to the BCS BEC Crossover Introduction Inclusion of Pairing Fluctuations Bogoliubov and Popov Approaches, and the Boson Boson Residual Interaction Results for Thermodynamic and Dynamical Quantities Thermodynamic Properties Dynamical Properties Concluding Remarks References The Unitary Gas and its Symmetry Properties Simple Facts About the Unitary Gas What is the Unitary Gas? Some Simple Properties of the Unitary Gas Application: Inequalities on n and Finite-Temperature Quantities Is the Unitary Gas Attractive or Repulsive? Other Partial Waves, Other Dimensions Various Models and General Relations Lattice Models and General Relations Zero-Range Model, Scale Invariance and Virial Theorem Two-Channel Model and Closed-Channel Fraction

4 Contents ix 5.3 Dynamical Symmetry of the Unitary Gas Scaling Solution in a Time-Dependent Trap SO(2,1) Dynamical Symmetry and the Decoupled Breathing Mode Separability in Internal Hyperspherical Coordinates Physical Consequences of the Separability Vanishing Bulk Viscosity Short-Range Scaling Laws Appendix 1: Effective Range in a Lattice Model Appendix 2: What is the Domain of a Hamiltonian? Appendix 3: Separability and Jacobi Coordinates for Arbitrary Masses Appendix 4: Hydrodynamic Equations Appendix 5: Alternative Derivation of the Vanishing Bulk Viscosity Appendix 6: n-body Resonances References Universal Relations for Fermions with Large Scattering Length Introduction The Tan Relations Tails of Distributions Changes in the Scattering Length Additional Tan Relations What is the Contact? Intuitive Interpretation Few-Body Systems Balanced Homogeneous Gas Strongly-Imbalanced Homogeneous Gas Other Universal Relations RF Spectroscopy Photoassociation Structure Factors Viscosity Spectral Functions Rapid Change in the Scattering Length Making Contact with Experiment Photoassociation Static Structure Factor Comparing Measurements of the Contact Tests of the Thermodynamic Tan Relations Contact Density Near Unitarity

5 x Contents 6.6 Derivations of Universal Relations Preliminaries Tan s Derivations Other Derivations Quantum Field Theory Derivations References Unitary Fermi Gas, Expansion, and Nonrelativistic Conformal Field Theories Introduction Expansion for the Unitary Fermi Gas Why Four and Two Spatial Dimensions are Special? Feynman Rules and Power Counting of Zero Temperature Thermodynamics Quasiparticle Spectrum Critical Temperature Phase Diagram of an Imbalanced Fermi Gas Aspects as a Nonrelativistic Conformal Field Theory Schrödinger Algebra Operator-State Correspondence Scaling Dimensions of Composite Operators Application of the Expansion General Coordinate and Conformal Invariance Vanishing Bulk Viscosities Superfluid Effective Field Theory Other Scale and Conformal Invariant Systems Appendix: Scaling Dimensions of Three-Body Operators Refernces Dilute Fermi and Bose Gases Introduction The Dilute Spinless Fermi Gas Dilute Classical Gas, k B Tk B T jlj; l\ Fermi Liquid, k B T l; l [ High-T Limit, k B T jlj The Dilute Bose Gas d \ d = The Dilute Spinful Fermi Gas: The Feshbach Resonance The Fermi-Bose Model Large N Expansion References

6 Contents xi 9 The Unitary Fermi Gas: From Monte Carlo to Density Functionals Introduction The Quantum Monte Carlo Approach From the Physical Problem to the Lattice Formulation Effective Hamiltonian The Hubbard Stratonovich Transformation Stabilization of the Algorithm for Small Temperatures Finite Size Scaling Results: The Energy and the Entropy Response to External Probes and the Spectral Function The Pairing Gap, Pseudogap, and Critical Temperature Describing Trapped Systems with Quantum Monte Carlo Results Density Functional Theory for the Unitary Fermi Gas The Energy Density Functional Determining the SLDA and ASLDA Energy Density Functionals Using the SLDA and ASLDA Time-Dependent Superfluid Local Density Approximation Time-Dependent Equations for the Quasiparticle Wave Functions Galilean Invariance The Excitation of the Pairing Higgs Mode Generation and Dynamics of Vortices Concluding Remarks Appendix References Scaling Flows and Dissipation in the Dilute Fermi Gas at Unitarity Introduction Scaling Flows Elliptic Flow Energy Dissipation Moments of the Navier Stokes Equation Scaling Solution of the Navier Stokes Equation Breakdown of Hydrodynamics Relaxation Time Approach

7 xii Contents 10.4 Expansion From a Rotating Trap Ideal Fluid Dynamics Dissipation Collective Oscillations Summary and Outlook References Thermodynamics of Fermi Gases Introduction Thermodynamics of Strongly Interacting Fermi Gases Thermodynamics in the Grand Canonical Ensemble and the Local Density Approximation Measuring the Local Pressure of a Trapped Fermi Gas The Zero Temperature Phase Diagram The BEC BCS Crossover Spin Imbalanced Gases and the Clogston Chandrasekhar Limit Beyond the Clogston Chandrasekhar Limit The Impurity Problem and the Polaron/Molecule Transition The Polarized Superfluid The Normal Phase Landau s Fermi Liquid Theory The Gas of Polarons The Fermi Liquid in the Unpolarized Limit The Normal/Superfluid Transition Line The Tricritical Point Fermi Liquid Versus Non-Fermi Liquid Molecular Limit Pseudogap High Temperature Expansion Conclusion Appendix References Normal Phase of Polarised Strongly Interacting Fermi Gases Introduction The N? 1 or Polaron Problem Homogeneous Case Non-Homogeneous/Trapped Case

8 Contents xiii 12.3 Unbalanced Fermi Gas or Many-Polaron Problem Homogeneous Case Non-Homogeneous/Trapped Case Different Mass Case: Fermi Mixture RF Spectroscopy Collisional Properties of the Normal Phase T = T = Experimental Consequences for Collective Modes Collective Oscillations: The Quadrupole Mode References Thermodynamics of Trapped Imbalanced Fermi Gases at Unitarity Introduction Ultracold Quantum Fields Bardeen-Cooper-Schrieffer Theory Fluctuations The Thermodynamic Potential Normal State Superfluid State Applications Interface and Surface Tension Deformation Conclusions References BCS BEC Crossover and Unconventional Superfluid Order in One Dimension Introduction BCS BEC Crossover of a Balanced One-Dimensional Fermi Gas Spin-Imbalanced Fermi Gas in One Dimension Bethe-Ansatz Solution for the Homogeneous Gas Phase Separation in a Trap FFLO Correlations in the Partially Polarized Phase Predictions From Bosonization Exact Numerical Results Spin- and Mass-Imbalanced Fermi Mixtures A Two-Channel Model: The Bose-Fermi Resonance Model Phase Diagram of the Bose-Fermi Resonance Model at Finite Imbalance

9 xiv Contents 14.7 Beyond 1D, Other Variations Proposals for the Experimental Observation of FFLO Correlations Summary References