Nonlinearities induced by parametric resonance in effectively 1D atomic Bose condensates

TL;DR

This paper numerically investigates how parametric resonance causes nonlinear effects in elongated Bose-Einstein condensates after a sudden change in trapping frequency, revealing phenomena like phonon pair loss, saturation, and atom depletion.

Contribution

It demonstrates that nonlinear dynamical effects in 1D Bose condensates can be effectively modeled and linked to cosmological preheating scenarios, highlighting new insights into condensate dynamics.

Findings

Exponential growth of resonant phonons matches Bogoliubov-de Gennes predictions

Loss of phonon pair nonseparability and atom depletion observed

Atomic spectrum becomes broad and incoherent, aligning with experiments

Abstract

We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the system. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking, as is the similarity of techniques used to study them.