Quantum fluctuations in trapped time-dependent Bose-Einstein condensates
Abstract
Quantum fluctuations in time-dependent, harmonically-trapped Bose-Einstein condensates are studied within Bogoliubov theory. An eigenmode expansion of the linear field operators permits the diagonalization of the Bogoliubov-de Gennes equation for a stationary condensate. When trap frequency or interaction strength are varied, the inhomogeneity of the background gives rise to off-diagonal coupling terms between different modes. This coupling is negligible for low energies, i.e., in the hydrodynamic regime, and an effective space-time metric can be introduced. The influence of the inter-mode coupling will be demonstrated in an example, where I calculate the quasi-particle number for a quasi-one-dimensional Bose-Einstein condensate subject to an exponential sweep of interaction strength and trap frequency.
Cite
@article{arxiv.0810.1347,
title = {Quantum fluctuations in trapped time-dependent Bose-Einstein condensates},
author = {Michael Uhlmann},
journal= {arXiv preprint arXiv:0810.1347},
year = {2009}
}