Quantum fluctuations in trapped time-dependent Bose-Einstein condensates

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 is 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 intermode coupling will be demonstrated in an example, where I calculate the quasiparticle number for a quasi-one-dimensional Bose-Einstein condensate subject to an exponential sweep of interaction strength and trap frequency.