Eur. Phys. J. D 19, 355-370 (2002)
https://doi.org/10.1140/epjd/e20020083

Basis-dependent dynamics of trapped Bose-Einstein condensates and analogies with semi-classical laser theory

¹ Foundation for Research and Technology Hellas, Institute of Electronic Structure and Laser, P.O. Box 1527, Heraklion 71110, Crete, Greece
² Department of Physics, University of Crete, Heraklion 71110, Crete, Greece

Corresponding author: ^a n.p.proukakis@durham.ac.uk

Received: 14 December 2001
Published online: 15 June 2002

Abstract

We present a consistent second order perturbation theory for the lowest-lying condensed modes of very small, weakly-interacting Bose-Einstein condensates in terms of bare particle eigenstates in a harmonic trap. After presenting our general approach, we focus on explicit expressions for a simple three-level system, mainly in order to discuss the analogy of a single condensate occupying two modes of a trap with the semi-classical theory for two-mode photon lasers. A subsequent renormalization of the single-particle energies to include the dressing imposed by mean fields demonstrates clearly the consistency of our treatment with other kinetic approaches.