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Journal of Experimental and Theoretical Physics

Photon cooperative effect in resonance spectroscopy

B. A. Veklenko

Published Aug 1, 1998• 0 citations
Publisher

Abstract

A systematic method is proposed for calculating the density matrix of subsystems interacting with their environment under conditions of thermodynamic equilibrium. The density matrix of photons resonantly interacting with a surrounding gas is calculated. It is shown that use of the Gibbs distribution allows one to completely eliminate inelastic processes from the calculations. A correct account of photon-photon correlators indicates the presence of new cooperative effects. A new branch of the polariton spectrum is predicted, which is due to the presence of excited atoms in the medium. With the help of the density matrix the mean filling numbers of the photon modes are calculated. In terms of wavelengths, we have obtained a generalization of the Planck formula which accounts for photon cooperative phenomena. The manifestation of these effects in kinetic processes is discussed.

DOI
10.1134/1.558656

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A systematic method is proposed for calculating the density matrix of subsystems interacting with their environment under conditions of thermodynamic equilibrium. The density matrix of photons resonantly interacting with a surrounding gas is calculated. It is shown that use of the Gibbs distribution allows one to completely eliminate inelastic processes from the calculations. A correct account of photon-photon correlators indicates the presence of new cooperative effects. A new branch of the polariton spectrum is predicted, which is due to the presence of excited atoms in the medium. With the help of the density matrix the mean filling numbers of the photon modes are calculated. In terms of wavelengths, we have obtained a generalization of the Planck formula which accounts for photon cooperative phenomena. The manifestation of these effects in kinetic processes is discussed.
A new method for calculating the density matrix of a quantized electromagnetic field which interacts with the environment in the presence of kinetic processes in the medium is suggested. This method accurately takes into account photon-photon quantum correlators and possesses certain symmetry properties, which substantially facilitate the summation of the Feynman diagrams that arise in the calculations. Forward scattering of resonance radiation by two-level gas atoms in a magnetic field is considered as an application. Insufficiency of a semiclassical description of this coherent process in excited media with the use of the unique tensor index of refraction is shown to follow from quantum electrodynamics. The introduction of one more function depending on the frequency of irradiation and the concentration of excited atoms is necessary. Experiments that simultaneously determine both this additional function and the standard refractive index of the medium are specified.
The influence of quantum interference between different decay channels of three-level atoms on various characteristics of matter and radiation is considered for the case of thermodynamic equilibrium of atoms in a photon gas. It is shown that for rare gases when collisions between atoms are not important, the direct consequence of such an interference is a spontaneously induced atomic coherence between two upper levels. Therefore, for an accurate description of such atoms and radiation in thermodynamic equilibrium with each other it is not sufficient to specify only Boltzmann exponents, which correspond to the diagonal elements of the density matrix. The reason for this is that the conventional Boltzmann description is applied to infinitely sharp eigenstates of the unperturbed Hamiltonian. As we show, it becomes essential to take into account nonzero width of the levels if the levels are relatively close to each other. This produces nonzero nondiagonal elements of the density matrix that modify the emissivity of the equilibrium medium and lead to a zero point at a certain frequency as well as to an enhanced intensity in the red wing at the corresponding temperature. It is shown that the occupation number of the photons is not changed and obeys the equilibrium Planck distribution.
The Dicke theory of coherent spontaneous emission is generalized by means of group-theoretical methods. Effects of superradiation and the structure of coherent responses of an equilibrium medium to pulsed excitation are considered. A method of calculating cooperative effects in second-order perturbation theory is developed. The role of collective properties of a system of radiators in experiments with high power exciting radiation is discussed. Some "anomalous" features of stimulated Raman scattering are accounted for.
Resonant two-photon absorption is discussed for the case in which the exciting field may be intense enough and near enough to resonance to cause appreciable saturation. A single pair of levels in an otherwise quite general atom is assumed to satisfy the appropriate resonance condition, and equations are derived governing the time evolution of the associated 2 \ifmmode\times\else\texttimes\fi{} 2 submatrix of the full atomic density matrix. Atomic relaxation is treated explicitly. The analysis, which treats both inversion-symmetric and inversion-nonsymmetric cases within the same general formalism, is developed systematically, the necessary approximations receiving careful discussion. The results are analogous to those for the corresponding one-photon process, but with a shift in the resonance frequency proportional to the intensity of the exciting field. This frequency shift is not identical to the one calculated by time-independent (second-order) perturbation theory, and becomes large when the energy of an intermediate state of the atom approaches the mean of the energies of the active states.
The theoretical approach takes in consideration the cooperative phenomena which appear between three particle in two-photon resonance in the process of single- and two- photon decay. This type of single- and two-quanta cooperative effect between three subsystems of radiators are described by master equation which takes into account three-particle cooperative resonance in the system. The resonance between the spontaneous emissions by two- and single photon transitions of three inverted radiators from the ensemble is proposed in order to accelerate the collective decay rate of the entangled photon pairs generated by the system. This effect is accompanied with the interferences between one-photon and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of three atomic correlation functions.
The excitation spectrum arising from photon density-density correlations has been considered in a system of two interacting identical atoms. The two-level atoms are pumped near resonance by a strong electromagnetic field while they interact through their dipole-dipole interaction and radiate to each other as well. In such a system the photon density-density correlations arise from the interference spectrum due to the beating of the frequency of the pump field and the atomic transition frequency, as well as from the spectrum induced by the dipole-dipole and radiative interactions between the atoms. The spectral function of this system has been calculated in the limit of high photon densities. It consists of four terms describing four bands which are similar to those appearing in the two-atom resonance fluorescence spectrum for the symmetric modes when the central peak is missing. The collective behavior as well as the dynamics of the system are discussed in detail. By using the spectral function, an expression for the photon density-density correlation function at different times has been derived where thermal effects have been also included.