Atomic Bose-Einstein condensation: Beyond mean-field theory

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

J. Rogel-Salazar, Seok Jin Choi, G.H.C. New +1 more

In this tutorial we present an introduction to some theoretical methods of quantum field theory applied to the description of a trapped Bose–Einstein condensate. First of all, we give a brief account of the main characteristics of the phenomenon of condensation and present the many-body Hamiltonian of the system. We outline some of the most important approaches used in the characterization of a condensed Bose gas, including the mean-field theory and the Hartree–Fock–Bogoliubov method. Finally we illustrate the use of these techniques addressing some important issues in quantum atom optics. We characterize the quantum state of a Bose–Einstein condensate (BEC) at zero temperature. We also describe a process of Beliaev coupling between quasiparticles using a method that includes terms beyond the usual Bogoliubov approach.

Guilherme Nunes

I present a new bosonic density functional especially conceived for the alkali atom Bose gas, together with the corresponding Kohn-Sham equation. The new formalism provides the simplest theory of the observed inhomogeneous Bose-Einstein condensate, beyond the level of mean-field theory.

Takafumi Kita

William Hoston

Nick P. Proukakis, Keith R. Burnett

We outline the general features of the conventional mean field theory for the description of Bose-Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with experimental data. We argue, however, that such an approach is not rigorous and cannot contain the full effect of collisional dynamics due to the presence of the mean field. We thus discuss an alternative microscopic approach and explain, within our new formalism, the physical origin of these effects. Furthermore, we discuss the potential formulation of a consistent finite-temperature mean field theory, which we claim necessitates an analysis beyond the conventional treatment. 1.