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Photonics

A Mode-Selective Control in Two-Mode Superradiance from Lambda Three-Level Atoms

Gombojav O. Ariunbold, Tuguldur Begzjav

Published Jul 3, 2025• 2 citations
Publisher

Abstract

Dicke superradiance, a single-mode burst of radiation emitted by an ensemble of two-level atoms, has garnered tremendous attention within the physics community. Its extension to multi-level systems introduces additional degrees of freedom, such as mode-selective control over well-known Dicke superradiant behaviors. However, previous work on the extension to two-mode superradiance in three-level atoms has been largely overlooked for over five decades. In this study, we revisit the two-mode superradiance model for a Λ-type three-level system, where two modes couple to a common excited state and two separate lower levels, offering new insights. For the first time, we obtain exact numerical solutions of the two-mode rate equations for this model. We analyze the temporal evolution of two-mode intensities, superradiance time delays, and quantum noise in the time domain as the number of atoms varies. We believe this work will enable external mode-selective control over superradiance processes—a capability unattainable in the single-mode case.

DOI
10.3390/photonics12070674

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Dicke superradiance, a single-mode burst of radiation emitted by an ensemble of two-level atoms, has garnered tremendous attention within the physics community. Its extension to multi-level systems introduces additional degrees of freedom, such as mode-selective control over well-known Dicke superradiant behaviors. However, previous work on the extension to two-mode superradiance in three-level atoms has been largely overlooked for over five decades. In this study, we revisit the two-mode superradiance model for a Λ-type three-level system, where two modes couple to a common excited state and two separate lower levels, offering new insights. For the first time, we obtain exact numerical solutions of the two-mode rate equations for this model. We analyze the temporal evolution of two-mode intensities, superradiance time delays, and quantum noise in the time domain as the number of atoms varies. We believe this work will enable external mode-selective control over superradiance processes—a capability unattainable in the single-mode case.
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.
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.
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.
We calculate the field eigenmodes of the superradiant emission from an ensemble of NNN two-level atoms and confirm the results of other authors that Dicke superradiant emission is restricted to a small number of modes, with more than 90% of the photons emitted in a single dominant mode. While numerical techniques are effective due to the symmetry of the problem, we develop also an analytical method to approximate the modes in the limit of a large number of emitters.
Superradiance, in which the collective behavior of emitters can generate enhanced radiative decay, was first predicted by a model, now known as the Dicke model, that contains a collection of two-level systems (the emitters) all interacting with the same photonic mode. In this article, we extend the original Dicke model to elucidate the influence of nuclear motion on superradiant emission. Our dynamical simulations of the combined electronic, nuclear, and photonic system reveal a new time scale attributed to the population leakage of the dark, subradiant states. Furthermore, this dark-state emission pathway can be controlled by tuning the nuclear potential energy landscape. These findings impact how superradiant states and molecular degrees of freedom can be leveraged and utilized in quantum optical systems.
The anticorrelated fluctuation of the intensity of a driver beam pumping a \ensuremath{\Lambda}-like three-level system in the first transition from the initial to the intermediate level and that of the intensity of the radiation generated in the second transition from the intermediate to the final level initiated by noise is observed in an experimental arrangement designed for the investigation of far-infrared Dicke's superradiance. The fluctuation is interpreted as the result of a two-photon back-and-forth transition between the initial and the final level, emitting (absorbing) and absorbing (emitting) photons in the first and the second transition depending on the direction of the two-photon transition. The influence of this two-photon back-and-forth transition on the Dicke's superradiance is discussed.