Driven Bose-Hubbard Model with a Parametrically Modulated Harmonic Trap

TL;DR

This paper explores how parametric modulation of a harmonic trap influences the stability and dynamics of a one-dimensional Bose-Hubbard system, revealing tunable resonance conditions and effective inhomogeneous hopping.

Contribution

It introduces a combined analytical and numerical approach to study the effects of global parametric driving on the Bose-Hubbard model, including a novel mechanism for controlling stability via atom interactions.

Findings

Parametric resonance can be tuned by interaction strength.

Global modulation induces effective inhomogeneous hopping.

The stability mechanism is confirmed for weak and strong interactions.

Abstract

We investigate a one-dimensional Bose-Hubbard model in a parametrically driven global harmonic trap. The delicate interplay of both the local atom interaction and the global driving allows to control the dynamical stability of the trapped quantum many-body state. The mechanism is illustrated for weak interaction by a discretized Gross-Pitaevskii equation within a Gaussian variational ansatz, yielding to a Mathieu equation for the condensate width. The parametric resonance condition can be tuned by the atom interaction strength. For stronger interaction, this mechanism is confirmed by results of the numerically exact time-evolving block decimation scheme. The global modulation also induces an effective time-independent inhomogeneous hopping strength for the atoms.