Mean field and correlated descriptions of Bose-Einstein condensates

Ying Wu, Xiaoxue Yang

We show that the evolution equations for mean quantities such as atom numbers and the inter-mode correlation for two-mode Bose–Einstein condensates form a closed set of equations in the SU(2) coherent state description, and they are identical in form to the two-mode mean-field model with only a slightly reduced two-body interaction strength. The exact analytical solutions to the evolution equations are also presented.

Alexandre B. Tacla, Carlton M. Caves

We investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection with the entanglement between the spatial degrees of freedom. We argue that the reduced dimensionality of the BEC is physically meaningful in a regime where spatial correlations are negligible. We handle the problem analytically within the mean-field approximation for general quasi-one-dimensional and quasi-two-dimensional geometries and obtain the optimal reduced-dimension, pure-state description of the condensate mean field. We give explicit solutions for the case of harmonic potentials, which we compare against exact numerical integration of the three-dimensional Gross-Pitaevskii equation.

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

William Hoston

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.