Full Gross-Pitaevskii Equation Research Articles

Symmetry breaking in Bose-Einstein condensates confined by a funnel potential

In this paper we consider a Bose-Einstein condensate in self-attraction regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted Pöschl-Teller potentials. The system is well described by a one-dimensional nonpolynomial Schrödinger equation, for which we analyze the symmetry break of the wave function that describes the particle distribution of the condensate. The symmetry break was observed for several interaction strength values as a function of the minimum potential well. In addition, we analyzed the symmetric and asymmetric solutions using a real-time evolution method, in which it was possible to confirm the stability of the results. Finally, a comparison with the cubic nonlinear Schrödinger equation and the full Gross-Pitaevskii equation were performed to check the accuracy of the effective equation used here.

Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.

Dynamical localization of matter-wave solitons in managed barrier potentials

The bright matter-wave soliton propagation through a barrier with a rapidly oscillating position is investigated. The averaged-over rapid oscillations Gross-Pitaevskii equation is derived, where the effective potential has the form of a finite well. Dynamical trapping and quantum tunneling of the soliton in the effective finite well are investigated. The analytical predictions for the effective soliton dynamics is confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schr{\"o}dinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasi-periodic oscillations of the DS about the minimum of the parabolic trap.