The characteristics of the cooperative cascade emission is studied by taking into account of the nonlinearity due to depopulation. It is shown that the emitted radiation exhibits considerably different behaviors in three regimes of the atomic number density. In the lowest density regime the radiation is essentially a quasi-stationary amplified spontaneous emission (ASE), in the intermediate one it becomes superradiant, and in the highest one it shows a new cooperative behavior peculiar to the cascade system. By using the present theory the experimental results recently observed in Li vapour is explained. It is also shown that the present theory describes the two-level cooperative emission as a specific limiting case.
In order to study the cooperative emission of radiation from an extended system of
N two-level atoms, we use the master-equation approach within the Born and Markov approximations. All the properties of the emission of radiation can be deduced from the diagonalization of the coupling matrix $\ensuremath{\Gamma}$, where an element ${\ensuremath{\Gamma}}_{\mathrm{jk}}$ gives the coupling between the atoms labeled
j and
k via the electromagnetic field. We choose a pencil-shaped volume and study analytically the coupling matrix in the limit for small and large Fresnel numbers. For Fresnel numbers of order unity numerical methods are used. Thus we prove that, for the pencil-shaped geometry, any elaborated model must take into account the interaction of the atoms with the infinity of electromagnetic field modes lying inside two small solid angles about the axis of the largest linear dimension, which we label the
z axis. In other words, the intensity of radiation emitted by any atom of the system depends on its position with respect to the others and this "propagation effect" cannot be neglected when interpreting superradiance experiments. For small Fresnel numbers the
z dependence predominates, in the opposite case the (
x,y) dependence does, while for Fresnel numbers of order unity the dependence of all three components must be taken into account. Preliminary calculations are given for which only the
z dependence is considered; for Fresnel numbers of magnitude of order unity or smaller, the effect of propagation along the
z axis displays large delays for the appearance of superradiance with respect to the time at which the superradiant pulse is maximum when the "propagation effects" are neglected (one-mode model).
We present a theory of cascade emission from an array of
N fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is
J=0, that of the intermediate state is
J=1, and that of the upper state is
J=0. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of
N atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.
In this paper the difference between two-photon dipole-forbidden and cascade transitions of an inverted system of atoms is studied. It is shown that the fluctuations of the electromagnetic field (EMF) density in the case of two-photon dipole-forbidden transitions are larger than the ones in the case of cascade emission. In the process of the two-photon dipole-forbidden cooperative emission the photons are created in pairs and there appears coherence between pairs of photons (biphotons). In this situation the distribution of energy between the photons in one pair may be random. For two-photon dipole-forbidden transitions the time-behavior of the square density fluctuations of EMF is similar to those of the density of EMF in the case of cascade emission. When the distance between two atoms excited relative to dipole-forbidden transitions is less than the radiation wavelength, then the kinetics of such atoms is analogous to the cascade emission of a single atom.
Expressions are derived for the intensity correlations or degrees of second-order coherence within and between two light beams of different frequency generated by cascade emission from a three-level atom. The atoms are assumed to be excited by two monochromatic coherent light beams in resonance with the upper and lower pairs of levels that constitute the triplet. The two emitted beams individually show photon antibunching and the correlation between the beams shows another complementary kind of non-classical effect. It is suggested that measurements on the system described here would provide more detailed information on quantum effects in cascade emission than previous observations with direct excitation to the uppermost atomic level by electron bombardment.
This paper investigates the dynamics of cooperative emissions in a cascade three-level system driven by an ultrashort laser pulse by solving numerically the full-wave Maxwell–Bloch equations. The 4, 4'-bis(dimethylamino) stilbene molecule is used as the model molecule because of its strong two-photon absorption property. The two-colour cooperative emissions are studied as functions of molecular number density and dephasing rate of the dipole coherence. The propagation effects on the evolution of the cooperative radiations are also taken into account. The cooperative radiations are enhanced for large number density of the molecule, while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiations and delays the emission times or even inhibits the formation of the emissions. The delay time of the radiation decreases with the increase of the molecular number density and the propagation distance.