Effect of trapping geometry on the parametric resonances in a disordered Bose-Einstein condensate driven by an...

We report parametric resonances (PRs) in a numerical investigation of a driven one-dimensional, interacting, and disordered Bose-Einstein condensate (BEC) confined in different traps. The BEC is excited by an oscillating Gaussian obstacle along a broad range of driving frequencies Ω. The PRs are detected via a quantity that is closely related to the time-average of the kinetic energy. The significant result of this work is that the trapping geometry plays a major role in defining the values of Ω at which PRs arise and controls their response to disorder. As such, it reveals the interplay of trapping geometry and disorder in these resonances. The dynamics of the modal coefficientC₀(t) as well as that of the phase-mismatchδ(t) between theC₀(t) andC₁(t) are examined at and away from PR. At PR, |C₀(t)| is generally found to be lower in magnitude than away from it, demonstrating that the atoms leave then= 0 ground state towards higher states. In the harmonic oscillator trap, the dynamic pattern ofδ(t) is found to be quite robust against changes in the disorder strength contrary to the box potential. This is because in the box the ratio of the random-potential and kinetic energies is higher than in the harmonic trap signaling that the influence of disorder is weaker in the latter.