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arXiv:2609.25359

Superradiant Mpemba Relaxation in a Dicke Ladder

Matheus G. H. Santos, Hugo Sanchez, Italo M. de Araújo, Luis Felipe A. da Silva, Miled H. Y. Moussa, Norton G. de Almeida

quant-phSubmitted Sep 21, 2026• Announced Sep 23, 2026• 0 citations
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Abstract

The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates $Γn(N-n+1)$. We construct the sparse family $ρ_A=|\lceil2N/3\rceil\rangle\langle\lceil2N/3\rceil|$ and $ρ_B=(|0\rangle\langle0|+|N\rangle\langle N|)/2$. Although $A$ is initially more energetic and more distant from the stationary ground state, it crosses $B$ in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from $N=6$ to $60$, while the peak intensities show an effective scaling close to $N^2$. The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.

Comments
3 figs, 5 pages

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The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates Γn(N−n+1)Γn(N-n+1)Γn(N−n+1). We construct the sparse family ρA=∣⌈2N/3⌉⟩⟨⌈2N/3⌉∣ρ_A=|\lceil2N/3\rceil\rangle\langle\lceil2N/3\rceil|ρA​=∣⌈2N/3⌉⟩⟨⌈2N/3⌉∣ and ρB=(∣0⟩⟨0∣+∣N⟩⟨N∣)/2ρ_B=(|0\rangle\langle0|+|N\rangle\langle N|)/2ρB​=(∣0⟩⟨0∣+∣N⟩⟨N∣)/2. Although AAA is initially more energetic and more distant from the stationary ground state, it crosses BBB in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from N=6N=6N=6 to 606060, while the peak intensities show an effective scaling close to N2N^2N2. The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
We study the dynamics of an ensemble of NNN two-level emitters undergoing collective decay at rate ΓΓΓ and collective incoherent pumping at rate RRR, confined to the fully symmetric Dicke ladder. Although the population dynamics are confined to a finite set of rate equations, their quantum-trajectory representation involves infinitely many pump-decay histories. We derive an exact finite continued fraction for the Laplace-transformed Dicke-state populations by resumming the infinitely many quantum trajectories generated by competing pump and decay processes. Our construction provides a physically transparent interpretation of the tridiagonal resolvent and extends to arbitrary permutationally symmetric initial states. In the strong- and weak-pumping regimes, we obtain perturbative transient solutions. We also identify exact relaxation eigenvalues and emission observables at balanced pump and decay strengths. Our solution provides a starting point for extending trajectory-based analytical methods to more general driven-dissipative collective systems.
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.
The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.
In Dicke superradiance, N identical two-level atoms in a small volume share one collective excitation ladder, and the ensemble discharges in a delayed burst whose peak grows in accordance with N2 rather than N. Real emitters, however, usually have more than two levels. When such an ensemble radiates cooperatively, its multiple decay channels interact rather than simply add up. This mini-review covers recent work that solves this interaction exactly for three-level atoms. We first recall the two-level benchmark: its exact delay statistics, their Gumbel-distributed fluctuation, and the resulting 21.7% deficit of the ensemble-averaged peak below the semi-classical estimate. The master-equation framework developed by Agarwal and Cho, Kurnit and Gilmore, on which the three-level results rest, comes next. The main part surveys three published papers, one for each of the three dipole-allowed three-level configurations. In the cascade, two emission pulses are correlated through an inherited timing. In the shared-source configuration, two channels compete for one atomic reservoir; for equal rates, as shown by Holzinger et al., this competition produces an exactly uniform terminal distribution, as in a Pólya urn. In the shared-sink configuration, two dynamically independent groups of atoms merge exactly into a single collective burst of the combined ensemble. We call this superradiant synthesis.
Dicke superradiance by an ensemble of quantum emitters produces a collective burst of radiation, but no entanglement in the mixed state of the emitters. We show that adding a local kinetic constraint between the emitters generates extensive mixed-state entanglement, while otherwise preserving all key features of Dicke superradiance. Specifically, for any local Boolean constraint, we analytically derive a lower bound for the emission rate which implies a peak intensity ∝N2\propto N^2∝N2 and a peak time ∝(log⁡N)/N\propto (\log N)/N∝(logN)/N with number of spins NNN. This effect enables the superradiantly accelerated preparation of entangled dark states. Hereby, Hilbert-space fragmentation of the Dicke ladder leads to an exponentially branching decay tree that generates a hierarchy of dark states. Importantly, these disconnected manifolds include exponentially many long-range entangled singlet dark states. The explored kinetic constraints and superradiant dynamics can be realized in neutral-atom arrays coupled to an optical cavity, and we suggest a simple and accessible witness to detect the predicted mixed-state entanglement in such experiments. Moreover, we show that entanglement generation is robust against atomic decay and collective dephasing, and should be observable under recently reported experimental conditions. Our results, thereby, offer a general framework and experimentally viable approach for the dissipative engineering of entangled dark states enhanced by superradiance.