Trap-modified Sakharov oscillations in a quenched BEC

In non-equilibrium dynamics of Bose systems, rich phenomena can emerge

such as Sakharov-like oscillations which connect quantum many-body

physics with cosmology. These oscillations in the atom density can be

created by quenching the interatomic interactions in a Bose condensate.

A previous study [Science 341, 1213 (2013)] has theoretically shown that

the oscillation frequencies depend on the momentum of the density

fluctuations following a Bogoliubov dispersion relation, in the absence

of a trapping potential. However, experimentally, there is a notable

discrepancy between the observed dispersion and the prediction when the

interaction is quenched up [Science 341, 1213 (2013)], which suggests

the indispensable role of the confining potential in this situation. In

our study, we investigate the density oscillations of a quenched BEC

confined within a harmonic potential. Our study explores both quench-up

and quench-down scenarios, varying the tunable interaction strengths. We

numerically and theoretically investigate these fluctuations using the

Gross-Pitaevskii equation (GPE). We examine the oscillation frequencies

of the low momentum mode (breathing mode), as well as those of the high

momentum (sound) modes. This addresses the way in which the dispersion

relations of the sound mode are modified by the trapping potential under

different quenching protocols.