Cooperative emission from a collection of atoms prepared in an initial state of complete inversion has been studied extensively in the past. In this paper we study the cooperative emission in dense atomic systems where there is a large average number of atoms per cubic resonance wavelength. For systems with such large densities, effects of the induced dipole-dipole interaction among neighboring atoms become important. Recently it has been shown that such interatomic interaction in a dense atomic system can lead to novel nonlinear effects.1,2 The induced dipole-dipole interaction for two-level atoms appears as a nonlinear inversion dependent renormalization of the atomic resonance frequency which gives rise to a set of modified Maxwell-Bloch equations. We study the phenomenon of superfluorescence (SF) and amplified spontaneous emission (ASE) using the modified Maxwell-Bloch equations. Statistical effects of amplified quantum stochastic processes are analyzed in SF and ASE. Phase wave statistics are analyzed in the linear regime of coherent pulse buildup. Amplified effects in the nonlinear regime in the SF to ASE transition region are statistically analyzed. Dipole dephasing due to collisions is found to play an important role.
The cooperative emission process in KCL;
O2${\mathrm{}}^{\mathrm{\ensuremath{-}}}$ has been studied as a function of the dephasing rate of the transition dipole. As the temperature of the sample is increased from 10 to 30 K, the emission evolves continuously from that characteristic of superfluorescence to that of amplified spontaneous emission. These results are in qualitative agreement with the predictions of current theories, but quantitative agreement is obtained only when current theories are modified so that the noise source that initiates the emission process is allowed to act continuously during the superfluorescent buildup.
We have studied the quantum-statistical properties of superfluorescence (SF) and amplified spontaneous emission (ASE) for dense media (media of densities corresponding to many atoms, on the average, within a cubic resonance wavelength). We use the Langevin equations of motion, obtained from a fully quantized model that takes into account induced near dipole-dipole interactions associated with dense media, together with the coupled Maxwell equation, to formulate a stochastic calculation ensemble. Quantum Monte Carlo methods are used in conjunction with the stochastic model, to conduct a statistical analysis of phase waves for this system. Results are presented for the phase-wave density, delay time, and peak-intensity fluctuations. The transition from SF to ASE is treated using the stochastic model.
We have developed a theoretical model that allows us to study the delay-time statistics of superfluorescent pulses for the case of collisional broadening with a Lorentzian line shape. Our model is based upon a more robust definition of delay time, based upon an energy rather than an intensity reference. We calculate the probability distribution of delay times in the initiation regime of superfluorescence, where the inversion is essentially constant. We find that, as the collisional dephasing rate is increased, the mean delay time increases and the distribution broadens. We compare our results with those for the case of inhomogeneous broadening with a Lorentzian line shape and find the unexpected result that the statistical behavior is identical.
We give a general nonperturbative treatment of cooperative emission in systems of
N two-level atoms, starting from first principles and including inhomogeneous broadening. In particular, we study superfluorescence, which is defined as the cooperative spontaneous emission, i.e., radiation rate proportional to
N2, from an atomic system initially excited with zero macroscopic dipole moment and a uniform population difference between the excited and the fundamental states. The atomic system is described by means of collective dipole operators. A fundamental justification is given for the existence of damped "quasimodes" of the mirrorless active volume. The damping of such modes is simply due to the propagation of the Maxwell field, which escapes from the active volume. A general atom-field master equation is derived for the system atoms plus field inside the active volume, described, respectively, in terms of collective dipole operators and quasimode operators. An important feature of this equation is that inhomogeneous broadening simply appears via a time-dependent atom-field coupling constant. In this paper we give a semiclassical treatment of such a master equation. For a pencil-shaped geometry of the active volume, generalized Maxwell-Bloch equations are derived for the envelopes of the radiation inside the active volume and polarization. Such equations take into account the two directions of propagation of the radiation and the inhomogeneous broadening. Suitably phrasing our initial condition in semiclassical terms, we find that propagation effects can be neglected at all times and the generalized Maxwell-Bloch equations reduce to a simple pendulum equation. On the basis of the discussion of the pendulum equation, we conclude that superfluorescence occurs when (i) the length
L of the active volume is much larger than a suitable threshold length
LT (this condition ensures that the dephasing atomic processes occur on a time scale much larger than the times characteristic of the cooperative emission); (ii) the length
L is smaller or of the same order of a suitable cooperation length
Lc (this condition ensures that cooperative spontaneous emission dominates stimulated processes, which give radiation proportional to
N). For $L\ensuremath{\ll}{L}_{c}$, one has a hyperbolic-secant superfluorescent pulse; for $L\ensuremath{\approx}{L}_{c}$, as one has in the recent experiments of Skribanowitz et al., one finds oscillations in the cooperative decay and in the radiation emission. Such oscillations are due to the contribution of stimulated processes. For $L\ensuremath{\gg}{L}_{c}$, this contribution increases. As a consequence one gets more oscillations in the radiated intensity, which becomes proportional to
N, so that superfluorescence effects disappear.
Metal halide perovskites (MHPs) have emerged as promising platforms for cooperative quantum emission. Superfluorescence is particularly intriguing because it arises from spontaneous synchronization of initially incoherent emitters into a macroscopic quantum state, producing delayed, intense, ultrafast bursts of coherent light. While superfluorescence has been demonstrated in perovskite nanocrystal superlattices and thin films, the mechanisms that enable its emergence at elevated temperatures, and the boundaries that separate cooperative from non-cooperative emission regimes, remain insufficiently understood.[1],[2] Addressing these knowledge gaps is essential for advancing superfluorescence toward quantum photonic applications.[3] In this talk, I present how our work tackles the challenges of identifying, and controlling superfluorescence in quasi-2D perovskite thin films. We demonstrate clear evidence to distinguish superfluorescence from amplified spontaneous emission and spontaneous emission. A comprehensive experimental phase map is constructed to reveal when and how macroscopic coherence forms, how it decays, and under what conditions it transitions into non-cooperative regimes.[4] Using quasi-2D PBA:CsPbBr3 thin films, we demonstrate superfluorescence with the lowest threshold fluence reported at 78 K in metal halide perovskites. Temperature and fluence dependent steady state and ultrafast spectroscopies resolve cooperative emission from 78 to 180 K, including a sharper coupled emission band, a delayed emission peak, ultrafast radiative lifetimes, quadratic like intensity scaling, and Burnham-Chiao ringing. We also map a phase diagram that delineates spontaneous emission, superfluorescence, and amplified spontaneous emission, and we observe deviations from ideal superfluorescence at high fluences and elevated temperatures, reflecting competing many-body and dephasing processes.[4] To interpret these observations, we introduce the ab initio quantum model Superfluorescence Non-Approximating Integrating Large Solver (SNAILS), which tracks emission density, inter emitter correlations, excited state populations, and trace distance under varying pumping and dephasing conditions.[4] Simulations reproduce delayed cooperative bursts when dephasing is weak and show rapid suppression of correlations and loss of delay when dephasing is stronger. Trace distance dynamics identify synchronization plateaus during cooperative emission and prolonged plateaus linked to subradiant or dark states under high dephasing, establishing a unified framework for cooperative emission and its breakdown in perovskite thin films. Overall, this work clarifies the optical and dynamical conditions required for macroscopic coherence in perovskites. The combined insights from phase mapping, ultrafast spectroscopy, and quantum modeling highlight strategies for lowering threshold fluence, mitigating dephasing, and extending superfluorescence toward higher temperatures.