Mean-field dynamics of two-mode Bose-Einstein condensates in highly anisotropic potentials: Interference, dimensionality, and entanglement

TL;DR

This paper develops a reduced-dimension mean-field model for two-mode Bose-Einstein condensates in highly anisotropic traps, incorporating effective interactions mediated by transverse degrees of freedom, and applies it to analyze phase dynamics and interferometry.

Contribution

It introduces a perturbative approach to derive effective 1D and 2D mean-field equations that include transverse effects for two-mode BECs in anisotropic potentials.

Findings

The model accurately describes the mean-field evolution of two-mode BECs in quasi-1D and quasi-2D geometries.

Numerical results show improved agreement with full 3D simulations over idealized models.

The approach provides insights into phase dynamics relevant for high-precision interferometry.

Abstract

We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of freedom can be decoupled from the dynamical equations at the expense of introducing additional effective three-body, attractive, intra- and inter-mode interactions into the dynamics of the loosely confined (longitudinal) degrees of freedom. These effective interactions are mediated by changes in the transverse wave function. The perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of a two-mode condensate in general quasi-1D and quasi-2D geometries. We use this model to investigate the relative phase and density dynamics of a two-mode, cigar-shaped $^{87}$Rb BEC. We study the relative-phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description.