Effect of trapping geometry on the parametric resonances in a disordered Bose–Einstein condensate driven by an oscillating potential

Abstract

We report parametric resonances (PRs) in a numerical investigation of a driven one-dimensional, interacting, and disordered Bose-Einstein condensate (BEC) con ned 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 signi cant result of this work is that the trapping geometry plays a major role in de ning 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 coef cient C 0 (t) as well as that of the phase-mismatch δ(t) between the C 0 (t) and C 1 (t) are examined at and away from PR. At PR, |C 0 (t)| is generally found to be lower in magnitude than away from it, demonstrating that the atoms leave the n = 0 ground state towards higher states. In the harmonic oscillator trap, the dynamic pattern of δ(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 in uence of disorder is weaker in the latter.

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

“…In one of our earlier publications [7], it has been verified that the effects on the BEC arising from the NGP with oscillating depth [Eq. (2)] are indeed similar to those from a(t) above if a bg < 0.…”

“…The signal energy is a term borrowed from engineering topics for the processing of an oscillating electrical signal. The signal energy has also been found very effective in revealing PRs in one of our earlier publications [2].…”

“…The time-modulation of the NGP depth in (2), that is δV DT (x, t) = δA cos(Ωt)e −βx 2 , generates an oscillating force along the length of the DBEC that is given by the potential gradient…”

“…The phenomenon of parametric resonances (PRs) is ubiquitious in nature and is a widely examined fundamental physical property. Today, PRs are one of the outstanding features observed in Bose-Einstein condensates (BECs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] where resonances are usually the result of modulating one of the system parameters such as the scattering length [11,[19][20][21][22]. They are also generated by external means such as a time-dependent trapping geometry [11], laser stirring [2], and laser-intensity modulation [1].…”

“…Today, PRs are one of the outstanding features observed in Bose-Einstein condensates (BECs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] where resonances are usually the result of modulating one of the system parameters such as the scattering length [11,[19][20][21][22]. They are also generated by external means such as a time-dependent trapping geometry [11], laser stirring [2], and laser-intensity modulation [1]. Moreover, PRs have been shown to occur in classical systems [23,24] as well as quantum devices such as birefringent optical fibers [25], magnetometers [26], superconducting wave guides [27], and quantum dots [28,29].…”