Quadrupole-scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates

TL;DR

This paper analyzes quadrupolar collective excitations and nonlinear mode coupling in two-component Bose-Einstein condensates, combining analytical predictions with numerical simulations to reveal complex nonlinear dynamics.

Contribution

It provides analytical resonance conditions for second harmonic generation and validates them through numerical simulations of coupled Gross-Pitaevskii equations.

Findings

Resonance conditions depend on trap aspect ratio and intercomponent interaction.

Numerical simulations confirm analytical predictions.

Nonlinear oscillations exhibit damping and recurrence similar to Fermi-Pasta-Ulam phenomena.

Abstract

We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. We obtain analytically the resonance conditions for the second harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.