Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates

TL;DR

This paper develops a time-dependent multi-orbital mean-field theory to describe the evolution of fragmented Bose-Einstein condensates, extending the traditional Gross-Pitaevskii approach to multiple occupied orbitals.

Contribution

It introduces the TDMF(n) theory for dynamic evolution of fragmented condensates with explicit equations for general interactions.

Findings

Derived the TDMF(n) equations for multiple orbitals.

Provided a numerical example demonstrating the theory.

Extended mean-field description beyond single-orbital models.

Abstract

The evolution of Bose-Einstein condensates is usually described by the famous time-dependent Gross-Pitaevskii equation, which assumes all bosons to reside in a single time-dependent orbital. In the present work we address the evolution of fragmented condensates, for which two (or more) orbitals are occupied, and derive a corresponding time-dependent multi-orbital mean-field theory. We call our theory TDMF($n$), where $n$ stands for the number of evolving fragments. Working equations for a general two-body interaction between the bosons are explicitly presented along with an illustrative numerical example.