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arXiv:2105.12844

Non-Equilibrium Steady States and Quantum Chaos in a three-site Driven-Dissipative Bose-Hubbard Chains base on Self-Consistent Mean-Field Approach

Chen-Huan Wu

Published May 26, 2021• 2 citations
arXivHTMLPDF

Abstract

We investigate the non-equilibrium dynamics and steady-state properties of a driven-dissipative Bose-Hubbard chain using a self-consistent Gutzwiller mean-field (GMF) approach. By employing a robust Picard iteration scheme, we solve the non-linear master equation for the non-equilibrium steady state (NESS) in the presence of strong Kerr nonlinearity. We identify two distinct dynamical regimes governed by the interplay between coherent drive, dissipation, and interaction: a regular quasilinear regime and a chaotic regime. Linear stability analysis reveals that the transition to the chaotic regime is triggered by parametric instabilities arising from the drive-induced coherence. Furthermore, we characterize the onset of quantum chaos by calculating the out-of-time-order correlator (OTOC). Our results show that in the strong coupling regime, the OTOC exhibits rapid exponential growth and saturation, providing a clear signature of information scrambling in this open quantum system. The proposed numerical framework offers an efficient pathway to explore many-body correlations in larger photonic lattices.

DOI
10.48550/arxiv.2105.12844

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Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms
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We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.