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Ukrainian Journal of Physics

Introducing the Generalized Absorptance for a Gas with Bound Atomic States

Андрій Сіжук, S. M. Yezhov

Published Mar 1, 2017• 2 citations
Publisher

Abstract

The quantum optical theory of absorption/reemission properties of a system of interacting atoms is discussed. The calculation method of the absorption coefficient is developed with regard for the quantization of field, thermal atomic motion, Doppler effect, and the model interaction between atoms. It is shown that the formulation of the absorption coefficient in the quantum optical context is based on the commutation relation between the operators of electric field and intensity. The revealed non-linear dependence of the absorption coefficient on the atomic density, even in the case of negligible binary interaction, can be referred to a certain kind of quantum-optic collective effects.

DOI
10.15407/ujpe62.03.0202

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The quantum optical theory of absorption/reemission properties of a system of interacting atoms is discussed. The calculation method of the absorption coefficient is developed with regard for the quantization of field, thermal atomic motion, Doppler effect, and the model interaction between atoms. It is shown that the formulation of the absorption coefficient in the quantum optical context is based on the commutation relation between the operators of electric field and intensity. The revealed non-linear dependence of the absorption coefficient on the atomic density, even in the case of negligible binary interaction, can be referred to a certain kind of quantum-optic collective effects.
Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.
A method of calculation of the absorption coefficient in the terms of quantum optics with regard for the quantization of the electromagnetic field and the Doppler effect is presented. It is shown that the local value of the absorption coefficient non-linearly depends on the atomic density and initial intensity. The analytically derived results are demonstrated in graphs for the the local absorption coefficient as a function of the frequency. The relatively strong dependence of the absorptance on the path length of an optical light beam is caused by the interatomic coupling through the intermediary of an electromagnetic field. The splitting of the absorption line induced by the Doppler effect in the system placed between mirrors is demonstrated.
The spatial inhomogeneity of absorption coefficient of the space between mirrors, filled by an optically active gas, is analyzed in quantum optical terms. It was theoretically shown, that the quantization of electromagnetic field in a cavity (optical resonator) can reveal the spatial inhomogeneity of absorption or re-emission ability of the optically active medium. It appears from the analytical calculations, the inhomogeneity is caused by the Doppler frequency shifts (including recoil effects) during the atom-photon collisions and the non-zero initial frequency width of the scanning signal. The proposed analytical representation of the absorption coefficient through the additive quantum optical terms gives deeper insight into intrinsic processes in the interacting with light matter.
Interactions of a quantized electromagnetic field In the preceding chapters we have studied the quantum properties of the electromagnetic field, but we have treated it as a free or non-interacting quantum system until now. However, both the emission and the absorption of light imply interactions with other quantum systems, and we now turn to the treatment of such interaction problems. It is true that, to a limited extent, we have already succeeded in treating some interactions of light in previous chapters, without invoking the full apparatus of the quantum theory of interacting systems. For example, in Chapter 9 the electromagnetic field was treated as a classical potential acting on an atomic quantum system, and in Sections 12.2 and 12.9 we invoked simple heuristic arguments to describe the operation of certain optical detectors. But these are limited applications, and, in any case, the validity of results obtained in this way needs to be confirmed. To describe the state of a quantized electromagnetic field (F) in interaction with some other quantum system (A), we evidently require an enlarged, or product Hilbert space, which encompasses both F and A, of which the Hilbert spaces of F and A are subspaces. We shall find it convenient to refer to the other system A as an ‘atomic system’, simply to give a name, without restricting the nature of A. The dynamical variables of the field Ô F( t ) and of the atomic system Ô A( t ) commute at the same time t , and at the beginning, when the interaction between them is assumed to be turned on, each operator acts only on the state vectors within its respective Hilbert space.
The structure of a solution of the generalized Maxwell–Bloch system of equations describing the strongly pumped interacting two-level atoms is discussed. This structure is represented by means of the corresponding differential equations for each contributing process. The interaction between the processes is introduced through the interaction integral and is illustrated by the specific system of graphs. The method allows one to describe the quantum-field-induced long-range interaction prevailing over short-range collisions and causing the broadening, narrowing, and shifts of an absorption line shape. The description is given in terms of the interaction integrals which couple the collective atomic polarization and population inversion. The contributions from different effects are analyzed with the use of the additivity of the corresponding absorption/reemission rates.
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.