Bose-Einstein Condensate Tunneling: The Gross-Pitaevskii Equation

K. S. Kleinbach

Li Gao-Qing, Chen Hai-Jun, Xue Ju-Kui +1 more

One-dimensional quantum tunneling dynamics between two-component Bose-Einstein condensates confined in a double-well magnetic trap is investigated. One-dimensional Gross-Pitaevskii equations for two-component Bose-Einstein condensates are derived from the three-dimensional ones. We derive Feynman equations from one-dimensional Gross-Pitaevskii equations. To study tunneling dynamics we solve Feynman equations in terms of a completely numerical procedure. In contrast to single-component condensates between two-component condensates, we find that this system can take on abundant tunneling results, the full tunneling dynamical behavior is summarized in phase portrait with constant energy lines. It is found that this system can achieve self-trapping when increase interatomic interactions exceed a critical value. We give the analytical critical expressions of interatomic interactions from the system Hamiltonian.

Carlos Trallero-Giner, J. F. Drake, Victor Lopez‐Richard +2 more

Rui‐Bin Liu, Mingyang Liu, Shizhong Zhang

Abstract We study the macroscopic quantum tunnelling of an interacting Bose-Einstein condensate in a cubic-plus-quadratic well that was approximately realized in recent experiment. We utilise the Gross-Pitaevskii equation and Wentzel-Kramers-Brillouin (WKB) method to investigate the effect of the inter-atomic interactions on the tunnelling rate of a quasi-bound condensate. We find that the existence of repulsive interaction enhances the quantum tunnelling of a trapped Bose-Einstein condensate.

Malek Abid, Cristián Huepe, Stéphane Métens +4 more

The Gross–Pitaevskii equation, also called the nonlinear Schrödinger equation (NLSE), describes the dynamics of low-temperature superflows and Bose–Einstein Condensates (BEC). We review some of our recent NLSE-based numerical studies of superfluid turbulence and BEC stability. The relations with experiments are discussed.

Rajendra K. Shrestha, Jun Ni, Wa Kun Lam +2 more