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arXiv:2508.13398 · Physical Review A

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

Leo Kruglikov, Filippo Ferrari, Vincenzo Savona

Published Nov 17, 2025• 3 citations
arXivHTMLPDF

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 multiphoton 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 $\text{U}(1)$ symmetry, photon saturation due to Kerr nonlinearity, and spatial prethermalization effects and a nonchaotic 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.

DOI
10.1103/dx11-jxbq

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We discuss dissipative chaos showing symmetries in the phase space and nonclassical statistics for a parametrically driven nonlinear Kerr resonator (PDNR). In this system an oscillatory mode is created in the process of degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. For chaotic regime we demonstrate, that the Poincaré section showing a strange attractor, as well as the resonator mode contour plots of the Wigner functions display two-fold symmetry in the phase space. We show that quantum-to-classical correspondence is strongly violated for some chaotic regimes of the PDNR. Considering the second-order correlation function we show that the high-level of photons correlation leading to squeezing in the regular regime strongly decreases if the system transits to the chaotic regime. Thus, observation of the photon-number correlation allows to extract information about the chaotic regime.
The emergence of equilibrium universality from intrinsically nonequilibrium dynamics is a fundamental open problem. Bose-Hubbard lattices realized in photonic and circuit-QED platforms provide a versatile setting to engineer nonlinear interactions, dissipation, and multiphoton processes. Here we investigate a Bose-Hubbard lattice subject to three-photon parametric driving, whose nonequilibrium steady state spontaneously breaks a Z3\mathbb Z_3Z3​ symmetry and realizes the criticality of the three-state Potts model, a three-state generalization of the Ising model. Using a variational phase-space approach with systematically controllable accuracy based on a Variational Multi-Gaussian ansatz, we perform finite-size scaling analyses in one and two spatial dimensions. We find that, in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the universality class of the 2D classical three-state Potts model. In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class. These results establish driven-dissipative bosonic lattices as a platform for emergent Potts criticality and identify multiphoton dissipation as a mechanism that promotes nonequilibrium critical behavior from classical to quantum universality classes.