Parametric excitations in a harmonically trapped binary Bose-Einstein condensate

TL;DR

This paper explores how periodic modulation of scattering lengths induces Faraday patterns in a two-component Bose-Einstein condensate, revealing complex density and spin pattern formations near the phase transition.

Contribution

It demonstrates the generation of density and spin Faraday patterns in a binary BEC through parametric excitation, including detailed analysis of pattern symmetry and growth rates.

Findings

Spin Faraday patterns exhibit out-of-phase density oscillations.

Pattern symmetry depends on the modulation frequency and condensate shape.

Growth rates vary with different modulation protocols.

Abstract

We investigate parametric excitation and pattern formation in a harmonically trapped two-component Bose-Einstein condensate. We assume the condensate to be in the miscible phase, but near the miscible-immiscible phase transition, where total density and spin density excitations are decoupled. By periodically modulating the atomic scattering lengths, Faraday patterns can be generated in both density and spin channels. In an elongated condensate, the pattern in the spin channel corresponds to a one-dimensional standing wave with the two components exhibiting an out-of-phase density oscillation, where the modulation frequency and the oscillation period are related to the velocity of the spin sound. After the spin pattern is fully developed, the system quickly enters a nonlinear destabilization regime. For a pancake-shaped condensate, a two-dimensional Faraday pattern is generated with an interesting l-fold rotational symmetry. The number of nodes along the radial and angular directions increases with larger modulation frequencies. We also compare the growth rates of spin Faraday patterns generated with different modulation protocols, which are accessible to current experiments.