$\mathcal{PT}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss

TL;DR

This paper investigates the phase transition related to $ ext{PT}$ symmetry in a one-dimensional Bose-Hubbard model with alternating gain and loss, analyzing both noninteracting and interacting regimes and how periodic modulation affects the symmetry.

Contribution

It provides an exact solution in the noninteracting case, constructs a phase diagram at the mean-field level for the interacting case, and demonstrates how modulation stabilizes the $ ext{PT}$-symmetric phase.

Findings

Interaction and dissipation induce $ ext{PT}$-symmetry breaking.

Periodic modulation stabilizes the $ ext{PT}$-symmetric regime.

Numerical results support the analytical phase diagram.

Abstract

We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{PT}$ symmetry under some specific conditions and features a $\mathcal{PT}$-symmetry phase transition. It is characterized by an order parameter corresponding to the population imbalance between even and odd sites, similar to the continuous phase transitions in the Hermitian realm. In the noninteracting limit, we solve the problem exactly and compute the parameter dependence of the order parameter. The interacting limit is addressed at the mean-field level, which allows us to construct the phase diagram for the model. We find that both the interaction and dissipation rates induce a $\mathcal{PT}$-symmetry breaking. On the other hand, periodic modulation of the dissipative coupling in time stabilizes the $\mathcal{PT}$-symmetric regime. Our findings are corroborated numerically on a tight-binding chain with gain and loss.