Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains

TL;DR

This paper explores how multi-photon drives influence the steady-state behaviors of dissipative bosonic chains, revealing chaotic and resonant regimes with implications for quantum state control.

Contribution

It introduces a detailed analysis of multi-photon driven bosonic chains, identifying distinct chaotic and resonant regimes and their underlying symmetries and dynamics.

Findings

Identification of a chaotic hydrodynamic regime with symmetry restoration

Discovery of a non-chaotic resonant nonlinear wave regime with quantum decoherence

Relevance for quantum state engineering in circuit QED platforms

Abstract

We investigate the steady-state dynamical regimes of boundary-driven, dissipative bosonic chains subjected to $n$-photon drives. Using the truncated Wigner approximation, we explore how multi-photon drives shape the interplay between quantum fluctuations, nonlinear interactions, and dissipative processes in such quantum systems. We identify two main regimes: a chaotic hydrodynamic regime characterized by the restoration of a local $\mathbb{U}(1)$ symmetry, photon saturation due to Kerr nonlinearity, and spatial prethermalization effects; and a non-chaotic resonant nonlinear wave (RNW) regime exhibiting sub-Poissonian photon statistics, persistent $\mathbb{Z}_n$ symmetry, and quantum-driven phase decoherence. Our findings reveal the universal nature of the hydrodynamic regime and highlight the RNW regime's sensitivity to boundary driving conditions, suggesting novel routes for quantum state engineering in driven-dissipative quantum devices. These results are experimentally relevant for state-of-the-art circuit quantum electrodynamics platforms.