Faraday and resonant waves in binary collisionally-inhomogeneous Bose-Einstein condensates

TL;DR

This study investigates how inhomogeneous interactions in binary Bose-Einstein condensates affect Faraday and resonant wave formation, revealing a transition to linear behavior and changes in wave properties as inhomogeneity increases.

Contribution

It demonstrates that increasing binary collision inhomogeneity causes the system to behave more linearly, altering wave periods and instability times based on initial ground state topology.

Findings

Stronger inhomogeneity leads to longer instability onset times.

The spatial period of waves decreases with increased inhomogeneity.

Ground state topology influences wave dynamics and instability timings.

Abstract

We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive numerical simulations that, as the system exhibits stronger spatially-localised binary collisions (whose scattering length is taken for convenience to be of Gaussian form), the system becomes effectively a linear one. In other words, as the scattering length approaches a delta-function, we observe that the two nonlinear configurations typical for binary cigar-shaped condensates, namely the segregated and the symbiotic one, turn into two overlapping Gaussian wave functions typical for linear systems, and that the instability onset times of the Faraday and resonant waves become longer. Moreover, our numerical simulations show that the spatial period of the excited waves (either resonant or Faraday ones) decreases as the inhomogeneity becomes stronger. Our results also demonstrate that the topology of the ground state impacts the dynamics of the ensuing density waves, and that the instability onset times of Faraday and resonant waves, for a given level of inhomogeneity in the two-body interactions, depend on whether the initial configuration is segregated or symbiotic.