We have studied the nature of the emission from a laser-excited KCI : O 2 − crystal and have observed that the emission evolves continuously from superfluorescence (SF) to amplified spontaneous emission (ASE) as the temperature of the crystal and hence the dephasing rate of the optical transition are increased. The sample is excited by a 30-ps pulse from a frequency-quadrupled Nd:YAG laser, and the 629.1-nm emission is detected using a streak camera system. At a temperature of 10 K the emission is characterized as SF with an average delay time of 200 ps and an average pulse width of 60 ps. As the temperature is increased to ~20 K, the output pulse broadens and the time delay increases to its maximum value of ~2 ns. As the temperature is increased still further, the time delay is observed to decrease, and at a temperature of 30 K the emission is characterized as ASE with a very small delay time and with an exponentially decaying time evolution. We modeled our experiment using the Maxwell-Bloch formalism and find good agreement for our measured output pulse shapes and for the dependence of delay time and pulse width on the dephasing rate.
We present a quantum-mechanical treatment of the influence of collisional dephasing processes on the statistical properties of superfluorescence (SF). The theory, which treats nonlinear propagation effects as well as quantum noise, shows how the nature of the cooperative emission process changes from that of SF to that of amplified spontaneous emission as the collisional dephasing rate is varied. The predictions of how the SF delay time varies with the collisional dephasing rate are in good agreement with the results of a recent experiment [M. S. Malcuit, J. J. Maki, D. J. Simkin, and R. W. Boyd, Phys. Rev. Lett. 59, 1189 (1987)].
Single crystals of KCl containing $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ centers (8\ifmmode\times\else\texttimes\fi{}
1016-7\ifmmode\times\else\texttimes\fi{}
1017 ${\mathrm{cm}}^{\ensuremath{-}3}$) were excited at low temperatures (
T<30 K) using frequency-quadrupled single pulses of a mode-locked Nd-doped yttrium aluminum garnet laser. At excitation intensities above 20 GW/
cm2 a spontaneous emission of coherent light was observed which could be identified as Dicke superfluorescence. This superfluorescence was observed on two of the zero-phonon lines in the vibrational progression of the $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ fluorescence spectrum (0-10 and 0-11 at 592.8 and 629.1 nm, respectively). We have studied the time dependence, the statistics of the delay times, and the intensities. The observed delay times vary between 0.5 and 10 ns, the observed pulse widths between 0.5 and 6 ns, and the coherence time was found to be longer than 100 ps. The observed linewidths of the superfluorescence ($0.016\mathrm{nm}\ensuremath{\cong}14\mathrm{GHz}$) is a factor of 2.5 smaller than that of the spontaneous fluorescence (0.042 nm at 4.2 K). The superfluorescence is observed only below a critical temperature which depends on the $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ concentration (8 to 28 K for concentrations between 8\ifmmode\times\else\texttimes\fi{}
1016 and 7\ifmmode\times\else\texttimes\fi{}
1017 ${\mathrm{cm}}^{\ensuremath{-}3}$).
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.
Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.
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.