Bogoliubov dynamics of condensate collisions using the positive-P representation

TL;DR

This paper develops a stochastic positive-P representation method to simulate the dynamics of colliding Bose-Einstein condensates, offering an efficient alternative to existing techniques especially for systems with limited particle numbers.

Contribution

It introduces a positive-P based approach for time-dependent Bogoliubov dynamics, improving efficiency and accuracy over traditional methods in certain regimes.

Findings

The method converges to the full Bogoliubov description with increasing realizations.

Numerical effort scales linearly with the lattice size.

It outperforms Wigner and exact positive-P methods when particle numbers are low.

Abstract

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realisations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-P methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation - when the total particle number in the system is insufficient for a truncated Wigner treatment.