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arXiv:2607.28034

Scaling theory of decoherence in Dicke superradiance

Nico S. Bassler, Julian Lyne, Javier Cuerda

quant-phcond-mat.stat-mechphysics.opticsSubmitted Jul 30, 2026• Announced Jul 31, 2026• 0 citations
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Abstract

The survival of many-body coherence depends on the competition between correlation buildup and decoherence. In Dicke superradiance, collective emission builds up correlations, producing a peak intensity scaling as $N^2$ for $N$ emitters. We develop a scaling theory including local dephasing and spontaneous emission and obtain fully collective, partially collective, and independent-emitter scaling regimes. The boundary of the fully collective regime defines a continuous phase transition in a transient observable. Local decoherence can prevent $N^2$ scaling despite increasing $N$.

Comments
5+11 pages, 3+4 figures

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The survival of many-body coherence depends on the competition between correlation buildup and decoherence. In Dicke superradiance, collective emission builds up correlations, producing a peak intensity scaling as N2N^2N2 for NNN emitters. We develop a scaling theory including local dephasing and spontaneous emission and obtain fully collective, partially collective, and independent-emitter scaling regimes. The boundary of the fully collective regime defines a continuous phase transition in a transient observable. Local decoherence can prevent N2N^2N2 scaling despite increasing NNN.
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states ∣j,m⟩|j,m\rangle∣j,m⟩ with distinct numbers of excitations n=m+jn=m+jn=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-NNN, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
Dicke superradiance describes an ensemble of N permutationally invariant two-level systems collectively emitting radiation with a peak radiated intensity scaling as N 2 . Individual Dicke states are typically entangled. However, the density matrix during superradiant decay is a mixture of such states, raising the subtle question of whether the total state is entangled or separable. We resolve this by showing analytically that for any N , starting from the fully excited state, the collective decay preserves separability for all times. This answers a longstanding question on the role of entanglement in Dicke superradiance and underscores that, despite collective dissipation, separable states remain separable under these dynamics.
We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.
Super-radiance is a striking phenomenon resulting from the collective interaction of emitters with light, and it is fundamentally related to the appearance of long-range correlations between the dipole moments of the emitters. As such, it represents a distinct phase of dissipative many-body systems compared to the case of independent emitters, similarly to how ferromagnetism stands out in magnetic materials in contrast to paramagnetism. In this work we address the conditions under which the transition to super-radiance can occur in ensembles of emitters subject to dephasing and individual decay -- a situation which is particularly relevant to the case of emitters in the solid state. The simplifying assumption of an ensemble of permutationally invariant emitters allows for the efficient solution of both the dissipative dynamics after a pulsed excitation, as well as of the steady state under incoherent pumping. This exact solution allows us to benchmark a truncated cumulant expansion approach, which can give predictions for arbitrarily big system sizes. We show that super-radiance is fundamentally robust to sizable dephasing and non-radiative decay rates, both under a pulsed excitation, as well as under continuous pumping. This robustness is the result of the collective acceleration effect of super-radiant emission with respect to the individual coupling to a local environment. We establish the universal critical scaling laws at the transition between normal radiance and super-radiance; and we show that, in the super-radiant phase, significant finite-size crossovers can be observed before reaching the asymptotic scaling regime. Our results pave the way for future experiments to provide a quantitative characterization of the scaling properties of super-radiance, seen as a distinct non-equilibrium many-body phase in ensembles of incoherently pumped emitters.
When a quantum system is put into an excited state, it will decay back to the ground state through a process termed spontaneous emission.It is generally assumed that spontaneous emissions between different individual emitters will not be coherent with each other; to produce coherent light, one would need population inversion and stimulated emission.In this work, we show that an optically thin ensemble of 11 000 radiating atoms spontaneously organizes to produce spatially coherent light.The reason for this coherence is collective coupling of the individual emitters via Dicke superradiance and subradiance (as opposed to amplification through stimulated emission).