Emerging Non-Hermitian Topology in a Chiral Driven-Dissipative Bose-Hubbard Model

TL;DR

This paper explores non-Hermitian topological phases in a driven-dissipative Bose-Hubbard model, revealing a phase diagram with topological amplification and potential implementation in superconducting circuits.

Contribution

It introduces a novel interacting model exhibiting non-Hermitian topological phases driven by coherent phase gradients and analyzes its steady states and phase diagram.

Findings

Identification of low- and high-density photon phases

Discovery of a phase coexistence region with topological amplification

Finite non-Hermitian winding number characterizing the topological phase

Abstract

We introduce a driven-dissipative Bose-Hubbard chain describing coupled lossy photonic modes, in which time-reversal symmetry is broken by a coherent drive with a uniform phase gradient. We investigate this model by means of a Gaussian variational ansatz and numerically prove that the steady-state solution is stabilized by an inhomogeneous profile of the driving amplitude, which damps out boundary effects. Our calculations unveil a non-equilibrium phase diagram showing low- and high-density phases for photons separated by a phase coexistence region in which the system exhibits the phenomenon of topological amplification and is characterized by a finite non-Hermitian winding number. Our work shows the emergence of non-Hermitian topological phases in an interacting model that can be naturally implemented with superconducting circuits.