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This research identifies a novel class of dissipative quantum systems where ordered coupling geometries in multimode Dicke models generate stable steady-states exhibiting Fibonacci scaling. The study demonstrates that these complex behaviors, including persistent oscillations, remain robust for finite cluster sizes using rigorous numerical methods like the hierarchy of pure states. Such findings expand our understanding of many-body phenomena accessible with current ultracold atom technologies and offer new pathways for engineering quantum optical cavities.
Fibonacci Steady-States and Persistent Oscillations in an Ordered Multimode Dicke Model
arXiv:2606.13072v1 Announce Type: new Abstract: Ultracold atoms in multimode optical cavities provide a rich testbed for many-body phenomena enabled by light-mediated interactions. Recent experiments include realizations of spin glasses and associative memories, as described by multimode Dicke models with disordered couplings. However, the properties of multimode Dicke models with ordered coupling geometries remain largely unexplored. In this work, we investigate the stable steady-states of the multimode Dicke model with an ordered nearest-neighbor coupling geometry, where $n_c$ atomic clusters are coupled via $n_c-1$ cavity modes. We show that the number of mean-field stable steady-states in the superradiant phase exhibits Fibonacci scaling with the number of atomic clusters, and that a subset of these steady-states exhibit persistent oscillations. Using both the truncated Wigner approximation and the numerically-exact hierarchy of pure states, we further demonstrate that these features of the stable steady-state solutions persist for finite cluster sizes. Ordered multimode Dicke models, such as the nearest-neighbor coupling geometry considered here, are accessible with current experimental technologies and point toward a broader class of strongly interacting dissipative systems with similarly rich behavior.
Abstract:Ultracold atoms in multimode optical cavities provide a rich testbed for many-body phenomena enabled by light-mediated interactions. Recent experiments include realizations of spin glasses and associative memories, as described by multimode Dicke models with disordered couplings. However, the properties of multimode Dicke models with ordered coupling geometries remain largely unexplored. In this work, we investigate the stable steady-states of the multimode Dicke model with an ordered nearest-neighbor coupling geometry, where $n_c$ atomic clusters are coupled via $n_c-1$ cavity modes. We show that the number of mean-field stable steady-states in the superradiant phase exhibits Fibonacci scaling with the number of atomic clusters, and that a subset of these steady-states exhibit persistent oscillations. Using both the truncated Wigner approximation and the numerically-exact hierarchy of pure states, we further demonstrate that these features of the stable steady-state solutions persist for finite cluster sizes. Ordered multimode Dicke models, such as the nearest-neighbor coupling geometry considered here, are accessible with current experimental technologies and point toward a broader class of strongly interacting dissipative systems with similarly rich behavior.
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2606.13072 [quant-ph]
(or arXiv:2606.13072v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.13072 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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