Improved Semiclassical Approximation for Bose-Einstein Condensates: Application to a BEC in an Optical Potential

TL;DR

This paper develops an improved semiclassical method for modeling Bose-Einstein condensates with various symmetries, enabling efficient and accurate approximations that incorporate three-dimensional effects, especially in quasi-one-dimensional configurations.

Contribution

It introduces a novel semiclassical approach for BECs that effectively captures 3D features in lower-dimensional models, including vortex solutions and nonlinear interactions.

Findings

Q1D solutions closely match full 3D results

Proper connection formulas improve accuracy in forbidden regions

Method effectively models vortex configurations

Abstract

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schrodinger equation, but the solution incorporates correct 3D aspects of the problem. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with full 3D and Thomas-Fermi ones are presented.