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

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 $\mathcal{P}\mathcal{T}$ symmetry under some specific conditions and features a $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetry breaking. On the other hand, periodic modulation of the dissipative coupling in time stabilizes the $\mathcal{P}\mathcal{T}$-symmetric regime. Our findings are corroborated numerically on a tight-binding chain with gain and loss.

8 pages, 7 figures

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• The physics of exceptional points
• Quantum trajectories and open many-body quantum systems
• A Straightforward Introduction to Continuous Quantum Measurement
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Quantum master equation with balanced gain and loss
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model