Dynamical quantum noise in Bose-Einstein condensates

TL;DR

This paper investigates dynamical quantum noise in Bose-Einstein condensates by deriving evolution equations and comparing simulation methods, highlighting stability issues in the positive-P approach and exploring the Wigner representation.

Contribution

It introduces a numerical simulation framework for quantum noise in condensates using phase space methods and compares positive-P and Wigner representations.

Findings

Positive-P approach shows stability problems in nonlinear regimes.

Wigner representation effectively simulates condensate evolution.

Comparison with single-mode models provides insights into quantum noise effects.

Abstract

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase space representations. We derive evolution equations for a single trapped condensate in both the positive-$P$ and Wigner representations, and perform simulations to compare the predictions of the two methods. The positive-$P$ approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate, and compare results to those for single-mode models.