Lectures by A.J. Leggett (Urbana) at U. Florida January/Feburary 2003
Lecture 1.Introduction
The idea of a "quantum liquid":the effects of quantization and
of indistinguishability
Basic facts about the systems of interest (alkali gases,4-He,3-He,
classical superconductors,cuprates)
The phenomenology of superfluidity and superconductivity.
Definition of (simple and "fragmented") BEC:condensate fraction,
superfluid velocity.Reasons for occurrence and stability of BEC.
The GP ansatz for a dilute Bose system.
Lecture 2.The simplest Bose-condensed system:ultracold alkali gases
(single-species case)
BEC of a noninteracting system in a harmonic trap.
The s-wave scattering length and the effective interaction:the
"factor of 2".GP ansatz for the alkali gases.
Experimental signatures of BEC:density profile,MIT interference
experiment,vortices.
Theoretical considerations concerning superfluidity in a dilute
spinless Bose gas (a toy model):experimental evidence for
superfluidity.
Brief introduction to the Bogoliubov theory.
Lecture 3:BEC in a multiple-species system.
The hyperfine degree of freedom in the alkali gases:GP description.
Interactions in a dilute multiple-species system (what happens to the
"factor of 2"?)
Ramsey-fringe experiments and phase diffusion.
Effect of hyperfine degree of freedom on supercurrent metastability.
The spin-1 case:the LPB state versus coherent (GP) states.
The spin-1/2 case:intrinsic fragmentation.
Some existing experiments on multiple-species alkali gases.
Lecture 4:Liquid 4-He.
Phenomenology of superfluidity in 4-He (recap)
London's hypothesis:evidence for BEC in He-II.(neutron sacttering,roton
evaporation).
The phonon-roton spectrum and some theoretical approaches to it (brief).
Explanation of the phenomena of superfluidity in terms of BEC
(including the deficiencies of the traditional Landau argument).
Liquid helium-4 in restricted geometries:Hohenberg's theorem,Landau-
Ginzburg description,"topological" superfluidity,Langer-Fisher and
Kosterlitz-Thouless mechanisms.
Lecture 5:Classical superconductivity
Phenomenology of superconductivity (recap)
Basics of the BCS pairing hypothesis:significance and structure of the
"pair wave function",relation to GL description.
Pair-breaking effects:the FFLO state.
Explanation of the Meissner effect and of supercurrent stability in
terms of pair condensation.
The Josephson effect at the macroscopic and mesoscopic levels:the
"Cooper-pair box".
Lecture 6:Superfluid liquid 3-He
The normal state of liquid 3-He:the phase diagram.
Cooper pairing in an anisotropic state:the spin and orbital degrees of
freedom,GL description.
The concept of spontaneously broken spin-orbit symmetry and its
consequences (NMR,orbital ferromagnetism,searches for parity
violation...)
Textures,vortices and flow in superfluid 3-He.
Nucleation of vortices and of the B phase;the experimental data and the
theoretical problem.
Lecture 7:Cuprate superconductivity
General description of the cuprtae superconductors:phenomenology of
cuprate superconductivity.
Anomalies of the normal state.
GL description,fluctuations.
What do we know _for sure_ about superconductivity in the cuprates?
Some existing theoretical approaches (brief).
How do we formulate the questions?A "back-door" approach to the problem
of cuprate superconductivity.
Lecture 8:BEC and related phenomena in an optical lattice
Basics of optical trapping and lattices.
The Munich and Florence experiments:alkali gases as analog computers
for solid-state problems.
Conceptual problems in the kinetics of BEC systems.
Lecture 9:Optional topics (at discretion of audience and lecturer)
Lecture 10:Overview
Common themes in the physics of alkali gases,helium,superonductors
What do we and don't we fundamentally understand about quantum liquids?
Tony Leggett,
Dept. of Physics,University of Illinois at Urbana-Champaign
Tel:(217)-333-2077
Fax: " " 9819