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arXiv:2605.15785

Dynamical aspects of steady-state subradiance: Detailed balance and its breakdown

Athreya Shankar, Simon B. Jäger, Jarrod T. Reilly, Raphael Kaubruegger, Murray J. Holland, Walter Hahn

quant-phcond-mat.stat-mechSubmitted May 15, 2026• Announced May 18, 2026• 0 citations
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Abstract

The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser is a paradigm system whose dynamics can be formulated as a Markov chain in a two-dimensional state space spanned by collective angular momentum states. In this article, we investigate the connection between a dissipative phase transition that occurs in the subradiant regime of this system in the large atom number limit, and the properties of the underlying Markov chain. In one of the phases, the Markov chain approaches the detailed-balance condition with increasing atom number $N$ and hence becomes effectively time-reversible. This is caused by a collective atomic emission process that effectively reduces the Markov chain to one dimension. In the other phase, we find the emergence of time-asymmetric probability currents in the two-dimensional state space that signals a breakdown of detailed balance. This is accompanied by a macroscopic internal entropy production rate in the Markov chain that scales extensively with the atom number $N$. An observable consequence of the probability currents is a self-pulsing of the cavity light output in this phase, which can be detected as an anti-correlation dip in the intensity correlation function.

Comments
7 pages, 5 figures, 2 pages appendix; comments welcome

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The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser is a paradigm system whose dynamics can be formulated as a Markov chain in a two-dimensional state space spanned by collective angular momentum states. In this article, we investigate the connection between a dissipative phase transition that occurs in the subradiant regime of this system in the large atom number limit, and the properties of the underlying Markov chain. In one of the phases, the Markov chain approaches the detailed-balance condition with increasing atom number NNN and hence becomes effectively time-reversible. This is caused by a collective atomic emission process that effectively reduces the Markov chain to one dimension. In the other phase, we find the emergence of time-asymmetric probability currents in the two-dimensional state space that signals a breakdown of detailed balance. This is accompanied by a macroscopic internal entropy production rate in the Markov chain that scales extensively with the atom number NNN. An observable consequence of the probability currents is a self-pulsing of the cavity light output in this phase, which can be detected as an anti-correlation dip in the intensity correlation function.
We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.
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We investigate collective behaviour that appears in open, many-body systems of two- and four-level atoms. Here, ``open" refers to the system interacting with an external environment that causes dissipation. We derive a general open quantum master equation to describe the system dynamics only, independent of this environment. We identify processes such as coherent exchange of virtual photons and modified decay rates caused by long-range interactions between all pairs of atoms that scale with distance by inverse power laws. We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the interatomic spacing is smaller than or comparable to the wavelength of light associated with the photon emitted from a given transition, virtual photon exchange interactions facilitate excitation transport through the chain. Atomic systems coupled to an environment display dissipative dynamics, however subradiant transport is exhibited from a variety of initial states; spontaneous emission from the chain occurs at a rate much slower than that for an individual atom. In particular, we find a region within the decay spectrum that consists entirely of subradiant states with a corresponding linear dispersion relation in the interaction energy. Identifying this subspace allows for the dispersionless transport of wave packets over long distances with near-zero decay. Moreover, the group velocity of the wave packet and direction of the transport can be controlled via an external uniform magnetic field while preserving its subradiant character. We discuss a number of experimental considerations to justify the feasibility and robustness of this protocol. Initial state preparation is outlined, utilising external laser driving to excite the system into the single excitation sector. Furthermore, we consider positional disorder by explicitly accounting for the external atomic degrees of freedom -- position and momentum -- which allows us to model the positions of all atoms by a motional state representing the occupation of a lattice well with a given width. These discussions are made in the low-temperature limit, where the atomic motion is essentially frozen, and we identify that subradiant transport is indeed robust. Finally, we explore the experimental limits of interatomic spacing and imperfect filling within an experimentally achievable optical lattice. We calculate the photon emission rate -- an experimentally measurable quantity -- and compare the emission spectra to our analysis. By limiting parameters to those achieved experimentally, we observe a reduction, yet not an absence, of collective behaviour. The simplicity and versatility of this system, together with the robustness of subradiance against disorder, makes it relevant for a range of applications such as lossless energy transport and long-time light storage. The lifetime of an atomic excitation could be increased by a factor of thousands to millions for a chain of atoms under the conditions that we explore in this thesis.
The emergent behavior that arises in many-body systems of increasing size follows universal laws that become apparent in order-to-disorder transitions. While this behavior has been traditionally studied for large numbers of emitters, recent progress allows for the exploration of the few-emitter limit, where correlations can be measured and connected to microscopic models to gain further insight into order-to-disorder transitions. We explore this few-body limit in the driven and damped Tavis–Cummings model, which describes a collection of atoms interacting with a driven and damped cavity mode. Our exploration revolves around the dressed states of the atomic ensemble and field, whose energies are shown to collapse as the driving field is increased to mark the onset of a dissipative quantum phase transition. The collapse occurs in stages and is an effect of light-matter correlations that are overlooked for single atoms and neglected in mean-field models. The implications of these correlations over the macroscopic observables of the system are presented. We encounter a shift in the expected transition point and an increased number of parity-broken states to choose from once the ordered phase is reached.
Cooperative effects such as super(or sub)radiance in quantum systems arise from the interplay among quantum emitters. While bright superradiant states have been extensively studied and have yielded important insights into cooperative phenomena, subradiant states remain less explored due to their inherently dark state nature. However, subradiance holds significant potential as a valuable quantum resource exploiting long-lived and large-scale entanglement, which is a key for advancing quantum information technologies. Here, we demonstrate strong collective emission from a cavity-mediated steady-state subradiant state. In a tailored photonic environment with balanced cavity dissipation, emitter-field coupling strength, and incoherent pumping, two quantum dots coupled to a low-Q cavity exhibit a steady-state population in a subradiant state with a highly negative cooperativity parameter among the emitters. As a key signature of steady-state subradiance, the system shows strong photon bunching ( g(2)(0)>8{{{\rm{g}}}}^{\left(2\right)}\left(0\right) > 8g(2)(0)>8 ) and suppressed single-photon decay (36 ns). Furthermore, we investigate that such collective interactions can be manipulated by controlling various system parameters, such as detuning and dephasing, supported by numerical simulations. Our approach to inducing cavity-mediated subradiance paves the way for generating and harnessing quantum correlations among quantum emitters via controlled dissipation. Subradiance is a cooperative effect in systems of quantum emitters, which is the opposite of superradiance, or enhanced emission, but has been less explored. Here, the authors demonstrate a steady-state subradiant state in a system of two InAs quantum dots coupled to a low-Q nanophotonic cavity.
Recently, strong coupling dominating dissipative and decoherence effects between the atom and a quantum cavity has been investigated experimentally. In this paper, we study the entanglement dynamics of two two-level atoms coupling to a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. We consider the effects of both Markovian dynamics and non-Markovian dynamics on the entanglement evolution of the two central atoms. Our results show that the steady entanglement can be generated between the two central atoms whether the system is under the Markov regime or non-Markov regime when the number of atoms of the atomic mirrors is finite. When the number of the atomic mirrors is large enough, the entanglement of two central atoms takes oscillating behavior without a stable value. The effect of detuning and dissipation on entanglement dynamics is also discussed and the results imply that the detuning plays an important role in improving the entanglement amplitude.