Number-Conserving Approaches for Atomic Bose-Einstein Condensates: An Overview

TL;DR

This paper reviews number-conserving methods for modeling atomic Bose-Einstein condensates, emphasizing their theoretical framework, implementation challenges, and applicability in accurately describing condensate dynamics.

Contribution

It provides a unified overview of number-conserving approaches, highlighting their advantages over traditional perturbative treatments for Bose-Einstein condensates.

Findings

Number-conserving methods maintain total atom number explicitly.

Framework unifies various existing approaches.

Discussion on implementation and validity of methods.

Abstract

Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultracold, trapped atoms, perturbative treatments to incorporate the non-condensate fraction are common. Here we describe how this may be carried out in an explicitly number-conserving fashion, providing a common framework for the work of various authors; we also briefly consider issues of implementation, validity and application of such methods.