Quantum master equation with balanced gain and loss

TL;DR

This paper introduces a quantum master equation for a Bose-Einstein condensate with balanced gain and loss, demonstrating that it captures PT-symmetric properties and aligns well with mean-field predictions even at small particle numbers.

Contribution

The work develops a quantum master equation that accurately describes a PT-symmetric Bose-Einstein condensate with balanced gain and loss, bridging many-particle and mean-field dynamics.

Findings

Stationary states and phase shifts are observed in the many-particle system.

Dynamics of the master equation agree with the Gross-Pitaevskii equation for small particle numbers.

The master equation effectively models PT-symmetric Bose-Einstein condensates.

Abstract

We present a quantum master equation describing a Bose-Einstein condensate with particle loss on one lattice site and particle gain on the other lattice site whose mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii equation. It is shown that the characteristic properties of PT-symmetric systems, such as the existence of stationary states and the phase shift of pulses between two lattice sites, are also found in the many-particle system. Visualizing the dynamics on a Bloch sphere allows us to compare the complete dynamics of the master equation with that of the Gross-Pitaevskii equation. We find that even for a relatively small number of particles the dynamics are in excellent agreement and the master equation with balanced gain and loss is indeed an appropriate many-particle description of a PT-symmetric Bose-Einstein condensate.