Dynamical instability of a Bose-Einstein condensate with higher-order interactions in an optical potential through a variational approach

TL;DR

This paper analyzes the dynamical instability of Bose-Einstein condensates with higher-order interactions in an optical lattice, combining analytical and numerical methods to derive instability conditions and effects of higher-order nonlinearities.

Contribution

It introduces a variational approach to study the impact of higher-order interactions on BEC stability within optical potentials, extending the standard Gross-Pitaevskii framework.

Findings

Higher-order interactions modify the modulational instability conditions.

Analytical results agree well with numerical simulations.

Higher-order nonlinearities influence the condensate dynamics significantly.

Abstract

We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.