Vortex formation and dynamics in two-dimensional driven-dissipative condensates

TL;DR

This paper explores the real-time dynamics of vortex formation and dissipation in two-dimensional driven-dissipative condensates using a phase space approach, revealing the persistence of vortex density beyond classical predictions.

Contribution

It introduces a phase space functional integral approach combined with the truncated Wigner approximation to study vortex dynamics in open quantum many-body systems.

Findings

Vortex-antivortex pairs are annihilated during dissipative cooling.

A finite vortex density persists at late times, contrary to vortex-free condensate predictions.

Quantum fluctuations beyond the truncated Wigner approximation are necessary for complete understanding.

Abstract

We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that governs the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi long-range order at late times. We observe that a finite vortex density survives the cooling process which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.