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arXiv:1404.7246 · Journal of Physics B Atomic Molecular and Optical Physics

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

Subramaniyan Sabari, R. Vasantha Jayakantha Raja, Kuppuswamy Porsezian, Paulsamy Muruganandam

Published Jun 3, 2010• 40 citations
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Abstract

We study the stabilization of a trapless Bose-Einstein condensate by analysing the mean-field Gross-Pitaevskii equation with attractive two- and three-body interactions through both analytical and numerical methods. Using the variational method we show that there is an enhancement of the condensate stability due to the inclusion of a three-body interaction in addition to the two-body interaction. We also study the stability of the condensates in the presence of the time-varying three-body interaction. Finally we confirm the stabilization of a trapless condensate from numerical simulation.

DOI
10.1088/0953-4075/43/12/125302

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We study the stabilization of a trapless Bose-Einstein condensate by analysing the mean-field Gross-Pitaevskii equation with attractive two- and three-body interactions through both analytical and numerical methods. Using the variational method we show that there is an enhancement of the condensate stability due to the inclusion of a three-body interaction in addition to the two-body interaction. We also study the stability of the condensates in the presence of the time-varying three-body interaction. Finally we confirm the stabilization of a trapless condensate from numerical simulation.
We investigate the nonlocal Gross–Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose–Einstein condensates (BECs). It is found that the dipolar BECs exhibit stability not only for the usual combination of attractive binary and repulsive three-body interactions, but also for the case when these terms have opposite signs. The trapless stability of the dipolar BECs may be further enhanced by time-periodic modulation of the three-body interaction imposed by means of Feshbach resonance. The results are produced analytically using the variational approach and confirmed by numerical simulations.
Abstract So far, attractive , trapless Bose–Einstein condensate (BEC) has been stabilized by considering the temporal modulation of the scattering length. However, there is no scope to stabilize the repulsive , trapless BEC even in the presence of the temporal modulation of the two-body interaction. However, in the present study, we stabilize the repulsive , trapless BEC by incorporating higher-order interaction. We also discuss the possibilities of the stabilization of repulsive, trapless BEC in the presence of time-varying higher-order interaction. Additionally, we verify our analytical findings by direct numerical simulation using the split-step Crank-Nicholson method.
We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.
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We study theoretically the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of the short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii equation with both constant and oscillatory forms of the short-range contact interaction along with long-range, nonlocal, dipole-dipole interaction terms. By using the variational method, we discuss the stability of the trapless dipolar BEC with the presence and absence of both constant and oscillatory contact interactions. We show that the oscillatory contact interaction prevents the collapse of the trapless dipolar BEC. We confirm the analytical prediction through numerical simulations. We also study the collective excitations in the system induced by the effective potential due to the oscillating interaction.
We investigate analytically and numerically the modulational instability of a Bose-Einstein condensate with both two- and three-body interatomic interactions and trapped in an external parabolic potential. Analytical investigations performed lead us to establish an explicit time-dependent criterion for the modulational instability of the condensate. The effects of the potential as well as of the quintic nonlinear interaction are studied. Direct numerical simulations of the Gross-Pitaevskii equation with two- and three-body interactions describing the dynamics of the condensate agree with the analytical predictions.