Semiclassical dynamics of atomic Bose-Einstein condensates

TL;DR

This paper investigates how classical a Bose-Einstein condensate (BEC) appears by comparing semiclassical equations with full quantum solutions, revealing that interactions reduce classicality but semiclassical models offer efficient and insightful approximations.

Contribution

It clarifies the limits of classical descriptions of BECs using semiclassical equations and demonstrates their effectiveness and computational efficiency compared to full quantum solutions.

Findings

Semiclassical equations capture many qualitative features of BEC dynamics.

Interatomic interactions decrease the classicality of BECs.

Semiclassical models are computationally less intensive than solving the GPE.

Abstract

An atomic Bose-Einstein condensate (BEC) is often described as a macroscopic object which can be approximated by a coherent state. This, on the surface, would appear to indicate that its behavior should be close to being classical. In this paper, we clarify the extent of how "classical" a BEC is by exploring the semiclassical equations for BECs under the mean field Gaussian approximation. Such equations describe the dynamics of a condensate in the classical limit in terms of the variables < x > and < p > as well as their respective variances. We compare the semiclassical solution with the full quantum solution based on the Gross-Pitaevskii Equation (GPE) and find that the interatomic interactions which generate nonlinearity make the system less "classical." On the other hand, many qualitative features are captured by the semiclassical equations, and the equations to be solved are far less computationally intensive than solving the GPE which make them ideal for providing quick diagnostics, and for obtaining new intuitive insight.