Dimensional reduction of a binary Bose-Einstein condensate in mixed dimensions

TL;DR

This paper derives effective lower-dimensional equations for a binary Bose-Einstein condensate with components in different spatial dimensions, enabling efficient analysis of static and dynamic properties in mixed-dimensional systems.

Contribution

The authors develop a binary effective nonlinear Schrödinger equation for mixed-dimensional BECs starting from 3D GPEs, validated against full 3D simulations.

Findings

Effective reduced equations match 3D GPE results well

Reduced models enable efficient numerical simulations

Applicable to systems with components in different dimensions

Abstract

We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as in a recent experiment [G. Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)]. Starting from a binary three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a Lagrangian variational approach we derive a binary effective nonlinear Schroedinger equation with components in different reduced dimensions, e. g., the first component in one dimension and the second in two dimensions as appropriate to represent a cigar-shaped BEC coupled to a disk-shaped BEC. We demonstrate that the effective reduced binary equation, which depend on the geometry of the system, is quite reliable when compared with the binary 3D GPE and can be efficiently used to perform numerical simulation and analytical calculation for the investigation of static and dynamic properties of a binary BEC in mixed dimensions.