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arXiv:2507.19467

Persistent subradiant correlations in a random driven Dicke model

N. V. Leppenen, Alexander N. Poddubny

Published Jul 25, 2025• 0 citations
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Abstract

We study theoretically the driven-dissipative dynamics of an array of two-level emitters, coupled to a single photonic mode, in the presence of disorder in the resonant frequencies. We introduce the notion of subradiant correlations in the dynamics, corresponding to the eigenstates of the Liouvillian with a low decay rate, that can also oscillate in time. While the usual collective subradiant states do not survive the emitter resonant frequency fluctuations, these subradiant correlations are immune to such a type of disorder. These long-living correlations exist in finite-size systems, when their lifetime is parametrically longer than in the so-called Dicke time crystal phase.

DOI
10.48550/arxiv.2507.19467

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We study theoretically the driven-dissipative dynamics of an array of two-level emitters, coupled to a single photonic mode, in the presence of disorder in the resonant frequencies. We introduce the notion of subradiant correlations in the dynamics, corresponding to the eigenstates of the Liouvillian with a low decay rate, that can also oscillate in time. While the usual collective subradiant states do not survive the emitter resonant frequency fluctuations, these subradiant correlations are immune to such a type of disorder. These long-living correlations exist in finite-size systems, when their lifetime is parametrically longer than in the so-called Dicke time crystal phase.
We theoretically study time-dependent correlations in a strongly driven array of NNN two-level atoms, coupled to photons in a waveguide. We focus on the spectrum {λ}\{λ\}{λ} of the Liouvillian superoperator, which determines the correlation decay rates −ℜλ-\Re λ−ℜλ and the frequencies ℑλ\Imλℑλ. Our main finding is the suppression of subradiant oscillating correlations between atomic states by a strong coherent drive of amplitude ΩΩΩ: ∣ℜλ∣≥mγ/2|\Re λ|\ge mγ/2∣ℜλ∣≥mγ/2, where γγγ is the single-atom spontaneous decay rate and m=∣ℑλ/(2Ω)∣m=|\Im λ/(2Ω)|m=∣ℑλ/(2Ω)∣ is a nonzero integer for correlations oscillating in time ∝exp⁡(±2im∣Ω∣t)\propto \exp(\pm 2i m|Ω| t)∝exp(±2im∣Ω∣t). This limit is independent of the number of atoms NNN; it holds both for small arrays and in the macroscopic limit. We demonstrate the suppression of subradiance numerically and provide a rigorous proof based on the analytical decomposition of the Liouvillian using spectral theory of simplicial complexes and posets.
The interplay between many-body interactions and controlled dissipation provides a rich setting for nonequilibrium quantum phases. We explore the superradiant phase transitions in a Rydberg-interacting open Dicke model with cavity loss and local dissipation. We find that the nonlinear feedback from atomic interactions stabilizes the atomic collective excited state and induces resonant collective motion, which can be further converted into robust superradiant oscillations with the inclusion of local dissipation. Beyond the mean-field approximation, we prove this system can support the finite-size local dissipative temporal order, i.e., continuous time crystal, from evidences of the decreasing damping of a finite-frequency Liouvillian mode and the linear-size scaling of quantum fluctuations. The correlation between the atomic colletive dynamics and the cavity photon number makes our findings easy to detect from output optical signal. By bridging interacting atomic matter and driven-dissipative cavity QED, our Rydberg-interacting Dicke model provides a unique spin-1/2 platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.
We study theoretically driven quantum dynamics in periodic arrays of two-level qubits coupled to the waveguide. We demonstrate, that strongly subradiant eigenstates of the master equation for the density matrix emerge under strong coherent driving for arrays with the anti-Bragg periods d=λ/4,3λ/4d=λ/4,3λ/4d=λ/4,3λ/4... This happens even though are no such states at low driving powers. Thus, our findings show that in the quantum nonlinear regime the domain of existence of subradiant states expands beyond conventional subwavelength structures. These driven states are directly manifested in long-living quantum correlations between the qubit excitations.
Atomic arrays can exhibit collective light emission when the transition wavelength exceeds their lattice spacing. Subradiant states take advantage of this phenomenon to drastically reduce their overall decay rate, allowing for long-lived states in dissipative open systems. We build on previous work to investigate whether or not disorder can further decrease the decay rate of a singly excited atomic array. More specifically, we consider spatial disorder of varying strengths in a one-dimensional (1D) half waveguide and in 1D, two-dimensional (2D), and three-dimensional (3D) atomic arrays in free space and analyze the effect on the most subradiant modes. While we confirm that the dilute half waveguide exhibits an analog of Anderson localization, the dense half waveguide and free-space systems can be understood through the creation of close-packed, few-body subradiant states similar to those found in the Dicke limit. In general, we find that disorder provides little advantage in generating darker subradiant states in free space on average and will often accelerate decay. However, one could potentially change interatomic spacing within the array to engineer specific subradiant states.
The collective behavior of ensembles of atoms has been studied in-depth since the seminal paper of Dicke [R. H. Dicke, Phys. Rev. 93, 99 (1954)], where he demonstrated that a group of emitters in collective states is able to radiate with increased intensity and modified decay rates in particular directions, a phenomenon which he called superradiance. Here, we show that the fundamental setup of two atoms coupled to a single-mode cavity can be distinctly exceeding the free-space superradiant behavior, a phenomenon which we call hyperradiance. The effect is accompanied by strong quantum fluctuations and surprisingly arises for atoms radiating out-of-phase, an alleged non-ideal condition, where one expects subradiance. We are able to explain the onset of hyperradiance in a transparent way by a photon cascade taking place among manifolds of Dicke states with different photon numbers under particular out-of-phase coupling conditions. The theoretical results can be realized with current technology and thus should stimulate future experiments.
Abstract The Dicke model—a paradigmatic example of superradiance in quantum optics—describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative nature of these interactions, the system’s dynamics is captured by the behavior of a single mean-field, collective spin. In this mean-field limit, it has recently been shown that the interplay between photon losses and periodic driving of light–matter coupling can lead to time-crystalline-like behavior of the collective spin (Gong et al 2018 Phys. Rev. Lett. 120 040404). In this work, we investigate whether such a Dicke time crystal (TC) is stable to perturbations that explicitly break the mean-field solvability of the conventional Dicke model. In particular, we consider the addition of short-range interactions between the atoms which breaks the collective coupling and leads to complex many-body dynamics. In this context, the interplay between periodic driving, dissipation and interactions yields a rich set of dynamical responses, including long-lived and metastable Dicke-TCs, where losses can cool down the many-body heating resulting from the continuous pump of energy from the periodic drive. Specifically, when the additional short-range interactions are ferromagnetic, we observe time crystalline behavior at non-perturbative values of the coupling strength, suggesting the possible existence of stable dynamical order in a driven-dissipative quantum many-body system. These findings illustrate the rich nature of novel dynamical responses with many-body character in quantum optics platforms.