Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

TL;DR

This paper investigates the dynamic behavior of a Bose-Einstein condensate in a combined harmonic and optical lattice trap, revealing how parametric resonances cause oscillation collapse and revival, influenced by the interplay of trapping potentials.

Contribution

It introduces a detailed analysis of parametric resonances in BECs under combined traps, highlighting the competition effects and conditions for resonance disappearance or instability.

Findings

Parametric resonances cause collapse and revival of BEC oscillations.

Resonances vanish when either the harmonic trap or optical lattice dominates.

Large optical lattice variations lead to exponential growth of Bogoliubov modes.

Abstract

In this work, we study parametric resonances in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric resonances (collapse and revival of the oscillations of the BEC width). Parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates. Parametric instabilities (exponential growth of Bogoliubov modes) arise for large variations in the strength of the optical lattice.