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

Topology in bosonic systems is often studied at the single-particle or semi-classical level, but less is known about the interplay between topology, interactions and dissipation. Driven-dissipative systems are ideal systems for studying such an interplay; in particular, Bose-Hubbard driven-dissipative lattices have been extensively investigated. This model consists of non-linear bosonic modes subjected to dissipation and coherent driving. Driven-dissipative Bose-Hubbard chains and lattices can be implemented in the quantum limit with superconducting circuits, microcavity polaritons and trapped ions.

A natural path to induce topological phases in quantum driven-dissipative systems is to break the time-reversal symmetry, an approach recently followed with the study of parametrically driven linear photonic lattices, in which non-trivial topology leads to the directional amplification of input signals. In this work we study a Bose-Hubbard chain in which time-reversal symmetry is broken by adding a site-varying phase to the coherent drive. We employ a Gaussian variational ansatz to approximate the density matrix and explore the emergence of non-Hermitian topological phases generated by the activation of parametric terms. Our main results are: (i) Stable steady-state solutions can be achieved by using an inhomogeneous profile for the coherent drive that dampens out boundary effects. (ii) The non-equilibrium phase diagram is divided into low and high boson density phases separated by a phase coexistence region. In the latter the system exhibits non-Hermitian topology and topological amplification properties. (iii) Within the phase coexistence region, quantum fluctuations are built up at the frontier between topological and trivial phases. (iv) Quantum correlations between sites are enhanced at the topological phase.