Using mixed many-body particle states to generate exact $\mathcal{PT}$-symmetry in a time-dependent four-well system

TL;DR

This paper demonstrates how mixed many-body states can be used to realize exact PT-symmetry in a time-dependent four-well Bose-Einstein condensate system, extending beyond mean-field approximations.

Contribution

It introduces a method to achieve exact PT-symmetry in many-body systems using mixed states, surpassing the limitations of pure states in mean-field models.

Findings

Exact PT-symmetry can be realized in many-body systems with mixed states.

Pure initial states cannot fully satisfy PT-symmetry conditions in the single-particle density matrix.

The approach extends PT-symmetry concepts beyond mean-field approximations.

Abstract

Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT-symmetric states. As proposed by Kreibich et al [Phys. Rev. A 87, 051601(R) (2013)], in the mean-field limit the dynamical behaviour of this system, especially that of the PT-symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate many-body effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for PT symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact PT symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.