Quantum fluctuations in trapped time-dependent Bose-Einstein condensates

TL;DR

This paper investigates quantum fluctuations in time-dependent trapped Bose-Einstein condensates using Bogoliubov theory, highlighting mode coupling effects and their impact on quasi-particle generation during parameter sweeps.

Contribution

It introduces an eigenmode expansion approach to analyze mode coupling in inhomogeneous, time-dependent BECs, extending understanding beyond the hydrodynamic regime.

Findings

Mode coupling affects quantum fluctuations during parameter changes.

An effective space-time metric describes low-energy excitations.

Calculated quasi-particle number during exponential parameter sweep.

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.