Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice

TL;DR

This paper explores nonequilibrium phenomena in driven-dissipative bosonic lattices, revealing how interactions and tilt lead to diverse stationary and dynamic states, including condensates, oscillations, and chaos.

Contribution

It introduces a detailed numerical analysis of a tilted driven-dissipative Bose-Hubbard model, uncovering novel nonequilibrium phases and dynamical regimes.

Findings

Bosons condense into a single Wannier-Stark state without Bloch oscillations at weak interactions.

Increasing interactions induce periodic Bloch oscillations and non-stationary regimes.

The phase diagram includes regular and chaotic dynamical behaviors.

Abstract

Driven-dissipative light-matter systems can exhibit collective nonequilibrium phenomena due to loss and gain processes on the one hand and effective photon-photon interactions on the other hand. As generic example we study a bosonic lattice system implemented via an array of driven-dissipative coupled nonlinear resonators with linearly increasing resonance frequencies across the lattice. The model also describes a driven-dissipative Bose-Hubbard model in a tilted potential without a particle-conservation constraint. We numerically predict a diverse range of stationary and non-stationary states resulting from the interplay of the tilt, tunneling, on-site interactions and loss and gain processes. Our key finding is that, under weak on-site interactions, the bosons mostly condense into a selected, single-particle Wannier-Stark state without exhibiting the expected Bloch oscillations. As the strength of the onsite interactions increase, a non-stationary regime emerges which, surprisingly, exhibits periodic Bloch-type oscillations. As a direct consequence of the driven-dissipative nature of the system we predict a highly nontrivial phase diagram including regular oscillating as well as chaotic dynamical regimes. While a straightforward photonic implementation using microwave or optical modes is possible, such dynamics might also be observable for an ultracold gas in a vertical lattice with gravity or a tilted external potential.