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Optics and Spectroscopy

Correlation of the energies of photons emitted in cascade transitions

P. S. Antsiferov

Published Feb 26, 2004• 0 citations
Publisher

Abstract

New details of a well-known physical process—cascade transition—have been considered. The wave function of a system of two photons emitted in a cascade transition in the absence of a shift of the phase of the intermediate state was studied. The joint energy distribution density for two such photons is obtained by numerical calculation, and a correlation between their energies at certain probabilities of radiative transitions is ascertained. This phenomenon can be used to diagnose the plasma density.

DOI
10.1134/1.1651252

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New details of a well-known physical process—cascade transition—have been considered. The wave function of a system of two photons emitted in a cascade transition in the absence of a shift of the phase of the intermediate state was studied. The joint energy distribution density for two such photons is obtained by numerical calculation, and a correlation between their energies at certain probabilities of radiative transitions is ascertained. This phenomenon can be used to diagnose the plasma density.
The question of the temporal correlation of photons arising from a three-level atomic cascade is considered by calculating the joint probability of photoelectric detection for two detectors placed in the far field of the atomic emission. The analysis is carried out in the Heisenberg picture and involves the use of dipole, adiabatic (Weisskopf-Wigner), and rotating-wave approximations. Except for a small interval about zero time delay, which is however too short to be detected, it is found that the temporal correlation between emitted photons is one of sequential but otherwise statistically independent events, even when Landau's generalized decay and frequency-shift terms are included. This result is compared with a well-known expression for the joint spectral density of the emitted photons.
The method for calculating the function of angular photon correlation and the angular distribution of photons emitted in the process of dielectronics recombination at any phase of a cascade of radiative and Auger transitions was presented. This method was developed incorporating the formalism of the spin density matrix and the kinetic Pauli equation as the basis. The calculations conducted revealed that the effect of alignment transfer in a cascade can have a strong impact on the shape of angular correlation of cascade photons.
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.
In a cascade three-level atomic system, a parametric study of sub-Poisson or super-Poisson distribution of a stimulated field was performed. By numerical calculation and figures, we investigated the time evolution of the sub-Poisson distribution of a radiation field. We found that different atomic initial states and different ratios of photon numbers of two radiation fields as well as different ratios of two transitions have a remarkable influence on this distribution. It is interesting to note that under certain conditions, in this cascade structure, there is a high degree of super-Poisson distribution that has not been reported in other structures. We try to explore this anomaly in detail.
We present a theory of cascade emission from an array of NNN fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is J=0J=0J=0, that of the intermediate state is J=1J=1J=1, and that of the upper state is J=0J=0J=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 NNN 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.
A theory of phase-matched cascade correlated emission is developed based on a source field approach. An ensemble of three-level atoms is prepared in a phased state for which the probability to have two excitations is negligibly small. The field intensity radiated on each of the transitions is calculated. The radiation on the upper transition is isotropic and unpolarized, but the phase-matched component on the lower transition can be directional and polarized. Moreover, for sufficiently high optical densities, the emission on the lower transition can be superradiant. In addition to the field intensities, the joint probability for emission on both transitions is calculated, exhibiting correlations in both the directions of emission and polarization of the fields.