Stability diagram and growth rate of parametric resonances in Bose-Einstein condensates in one-dimensional optical lattices

TL;DR

This paper analyzes the stability and growth rates of parametric resonances in Bose-Einstein condensates within one-dimensional optical lattices, using linearized GP equations and simulations, with implications for spectroscopy and quantum fluctuation amplification.

Contribution

It provides a detailed calculation of the stability diagram and growth rates of parametric resonances, confirming previous findings and exploring quantum fluctuation amplification beyond GP theory.

Findings

Agreement between linearized GP results and time-dependent simulations

Identification of seed excitation roles in parametric amplification

Potential applications in spectroscopy and quantum thermometry

Abstract

A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim (M. Kraemer et al., Phys. Rev. A (2005) in press) concerning the key role of parametric resonances in the response observed by Stoeferle et al. (Phys. Rev. Lett. 92, 130403 (2004)) in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry.