Instability of Bose-Einstein condensates in tilted lattices with time-periodical modulation

TL;DR

This paper investigates the dynamical stability of Bose-Einstein condensates in optical lattices under combined periodic modulation and constant acceleration, revealing how resonance conditions affect stability thresholds and unstable regions.

Contribution

It provides explicit quasienergy expressions and stability diagrams, analyzing the effects of integer and non-integer resonances on condensate stability, which was not previously detailed.

Findings

Critical interaction strength varies with resonance type.

Unstable regions are linked to negative effective tunneling.

Stability behavior differs between integer and half-integer resonances.

Abstract

We study the dynamical stability of Bose-Einstein condensates in an optical lattice with a time-periodic modulation potential and a constant acceleration force simultaneously. We derive the explicit expressions of quasienergies and obtain the stability diagrams in the parameter space of the interaction strength and the modulation amplitude. The ratio of the acceleration force to the modulation frequency characterizes two cases: integer and non-integer resonances. For integer resonances, the critical interaction strength $g_{\mathrm{c}}$ shows an alternate behavior where the completely unstable regions correspond to the negative effective tunneling strength. Among non-integer resonances, we observe that $g_{\mathrm{c}}$ peaks are centered around half-integer resonances for which the completely unstable regions disappear, accompanied with a whole displacement of $g_{\mathrm{c}}$. Compared with integer and half-integer resonances, the crossovers between them show no explicit dependence of $g_{\mathrm{c}}$ on the modulation amplitude.