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arXiv:2504.13418 · Physical Review Letters

Unraveling Dicke Superradiant Decay with Separable Coherent Spin States

Pedro Rosário, Luiz O. R. Solak, A. Cidrim, Romain Bachelard, Johannes Schachenmayer

Published Jul 28, 2025• 10 citations
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Abstract

We show that idealized Dicke superradiant decay from a fully inverted state can at all times be described by a positive statistical mixture of coherent spin states (CSS). Since CSS are separable, this implies that no entanglement is involved in Dicke decay. Based on this result, we introduce a new numerical quantum trajectory approach leading to low-entanglement unravelings. This opens up new possibilities for employing matrix product state (MPS) techniques for large-scale numerical simulations with collective decay processes.

DOI
10.1103/xcxr-sm9c

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We show that idealized Dicke superradiant decay from a fully inverted state can at all times be described by a positive statistical mixture of coherent spin states (CSS). Since CSS are separable, this implies that no entanglement is involved in Dicke decay. Based on this result, we introduce a new numerical quantum trajectory approach leading to low-entanglement unravelings. This opens up new possibilities for employing matrix product state (MPS) techniques for large-scale numerical simulations with collective decay processes.
We study the collective decay of an initially inverted ensemble of two-level emitters in two distinct scenarios: when coupled to a squeezed photonic reservoir and when interacting with a one-dimensional waveguide. Using a quantum-state diffusion approach to unravel the emission process, we investigate entanglement and classical correlations along individual quantum trajectories over time. This numerical analysis shows that despite an initial buildup of entanglement and a significant amount of entanglement due to either spin squeezing or dark states at late times, the essential features of the superradiant burst are well described by averages over fully factorizable states. We explain this observation in terms of an almost complete factorization of all 2-local observables, which we identify as a generic property of superradiant decay. Based on this insight, we provide a purely classical theory for the burst in squeezed superradiance, which is both intuitive and exact for a large number of emitters. Moreover, we find that our numerical approach also performs well in the presence of subradiant states, which dominate the slow residual decay of nonuniform ensembles at late times.
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.
Collective superradiant decay of a tightly packed inverted quantum emitter ensemble is among the most intensely studied phenomena in quantum optics. Since the seminal work of Dicke more than half a century ago, a plethora of theoretical calculations in quantum many-body physics have followed. Widespread experimental efforts range from the microwave to the X-ray regime. Nevertheless, accurate calculations of the time dynamics of the superradiant emission pulse still remain a challenging task needing approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a new, recently found exact solution. Applying two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The longterm population evolution is only correctly captured for low emitter numbers, where an individual spin-based cumulant expansion proves more reliable than the collective spin-based variant. Surprisingly, odd orders show even qualitatively nonphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, at a longer time scale, the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when applied for long-time evolution or reliably finding steady states.
Collective superradiant decay of a tightly packed inverted quantum emitter ensemble is among the most intensely studied phenomena in quantum optics. Since the seminal work of Dicke more than half a century ago, a plethora of theoretical calculations in quantum many-body physics have followed. Widespread experimental efforts range from the microwave to the X-ray regime. Nevertheless, accurate calculations of the time dynamics of the superradiant emission pulse still remain a challenging task requiring approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a newly found exact solution. The application of two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The long-term population evolution is only correctly captured for low emitter numbers, where an individual spin-based cumulant expansion proves more reliable than the collective spin-based variant. Surprisingly, odd orders show unphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, on longer time scales the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when used for long-time evolution or reliably finding steady states.
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.
We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of NNN identical two-level systems undergoing collective spontaneous emission. This serves as one of the simplest cases of open quantum system dynamics that allows for a fully analytical solution. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of spins. These approaches range from solving coupled rate equations and identifying exceptional points in non-Hermitian evolution to employing combinatorial and probabilistic techniques, as well as utilizing a quantum jump unraveling of the master equation. The analytical solution is expressed as a residue sum obtained from a contour integral in the complex plane, suggesting the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.