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Photonics

A Mini-Review: Cooperative Spontaneous Emission from Two- and Three-Level Atoms

Munkh-Uchral Bazarsan, Mend-Amar Lutsukh, Tuguldur Begzjav, Gombojav O. Ariunbold

Published Sep 30, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.3390/photonics13100933

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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.
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. 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 λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. 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.
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 investigate the collective dynamics of a three-level ensemble under the Dicke limit, revealing a unified connection between superradiant emission and electromagnetically induced transparency (EIT). Our results show that the transient superradiant burst exhibits the expected peak intensity scaling Imax⁡ ⁣∼ ⁣N2I_{\max}\!\sim\! N^2Imax​∼N2, with a universal finite-size correction ∣ξ(N)−2∣ ⁣∼ ⁣1/ln⁡N|ξ(N)-2|\!\sim\! 1/\ln N∣ξ(N)−2∣∼1/lnN that governs the apparent scaling exponent in realistic ensembles. In the stationary regime, collective broadening modifies the EIT response: although it typically enhances absorption, it counterintuitively increases the group velocity, leading to a relative scaling vg ⁣∝ ⁣N2v_g\!\propto\! N^2vg​∝N2, even while vg ⁣≪ ⁣cv_g\!\ll\! cvg​≪c. This effect suggests that cooperative interactions fundamentally limit the achievable slow-light delay in dense media. To achieve these results, we derive a representative-atom master equation that quantitatively reproduces both the superradiant and EIT regimes, in excellent agreement with the exact symmetric-subspace dynamics and correctly incorporating collective feedback and NNN-dependent broadening. This unified framework bridges transient superradiant emission and steady-state quantum interference, with direct implications for slow light, quantum memories, and precision metrology.
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.
We experimentally investigate the collective radiative decay of a fully inverted ensemble of two-level atoms for a chiral, i.e., propagation direction-dependent light-matter coupling. Despite a fundamentally different interaction Hamiltonian which has a reduced symmetry compared to the standard Dicke case of superradiance, we do observe a superradiant burst of light. The burst occurs above a threshold number of atoms, and its peak power scales faster with the number of atoms than in the case of free-space Dicke superradiance. We measure the first-order coherence of the burst and experimentally distinguish two regimes, one dominated by the coherence induced during the excitation process and the other governed by vacuum fluctuations. Our results shed light on the collective radiative dynamics of cascaded quantum many-body systems, i.e., systems in which each quantum emitter is only driven by light radiated by emitters that are upstream in the cascade. Our findings may turn out useful for generating multiphoton Fock states as a resource for quantum technologies. Published by the American Physical Society 2024
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.