Bose Condensation - Single View

The lecture starts online, coordinate parameters available on Moodle.

Bose predicted in the 1920s that an ideal gas of particles with integer spin should occupy the state of lowest energy with a macroscopic particle number, forming the so-called Bose-Einstein condensate. In the 1950s, this concept helped to understand the superfluidity of liquid He and superconductivity (condensation of Cooper pairs). In the 1990s, experiments with ultracold atomic gases provided the first realisations of weakly interacting Bose gases that can be excellently compared with theory.

We present the corresponding experiments and a panorama of theoretical frameworks:

– statistical mechanics of ideal gases in traps

– Pensore-Onsager criterion for condensation, correlation functions

– mean-field theory for the interacting Bose gas (nonlinear Schrödinger or Gross-Pitaevskii equation)

– Bogoliubov theory for elementary excitations and finite temperatures, superfluidity, equation of state

– the Yang-Yang solution for the Lieb-Liniger model of 1D Bosons at finite temperature

– mapping to a classical random walk in the complex plane: counting statistics

– nonlinear stochastic Gross-Pitaevskii equation for dynamics at finite temperature

– experiments: Feshbach resonances, optical lattices, atom laser

Approaches: analytical theory, numerical calculations, stochastic simulations