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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Cooperative optical response of a two-layer resonant system

Igor Viktorovich Ryzhov, А. И. Зайцев

Published Mar 3, 2008• 0 citations
Publisher

Abstract

According to the semi classical approximation (neglecting quantum correlations between the field and atoms)we investigate resonant and nonresonant optical effects arising in the two-layer medium that consists of three-level atoms with the A-scheme of optical transitions which are prepared so that they can undergo a super-radiant decay of their electronic states. The analytic regularities related to a linear stage of development of super-radiation in high-frequency optical channels of the medium under consideration are given in the article. Raman effect related to doublet structure of the lower level is analyzed.

DOI
10.1117/12.801682

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According to the semi classical approximation (neglecting quantum correlations between the field and atoms)we investigate resonant and nonresonant optical effects arising in the two-layer medium that consists of three-level atoms with the A-scheme of optical transitions which are prepared so that they can undergo a super-radiant decay of their electronic states. The analytic regularities related to a linear stage of development of super-radiation in high-frequency optical channels of the medium under consideration are given in the article. Raman effect related to doublet structure of the lower level is analyzed.
A cavity-like regime of superradiance for a double-layer medium populated by atoms with the A-scheme of transitions is considered in a semiclassical approximation under the condition that the layers are arranged symmetrically with respect to initial characteristics of the field and atomic system populating the layers. An analytical law for the linear stage of the superradiance process is found that agrees well with numerical solution of the differential equations of the model under consideration for any initial conditions nearly up to the peak of the appropriate characteristic of the field intensity module. For the case of degenerate lower doublet, the resonant character of the dependence of the superradiance pulse time delay on the distance between the layers is studied.
The two-photon and scattering resonances between the spontaneous emissions of the two- and single- photon transitions of the three-level inverted radiators in the Ξ, V configurations and the system of two-level radiators D, inverted relatively the dipole forbidden transition are revised. This approach opens the new possibilities in the manipulation of the decay process and generation of the entangled photon pairs. The correlation between the V and Ξ cascade three-level subsystems on the two-photon transitions of dipole forbidden radiators is studied, taking into consideration the cooperative scattering and two photon resonances through the vacuum field. One of them corresponds to the situation when the total energy of emitted photons by three level dipole-active radiator in the cascade configuration enters into the two-photon resonance with the dipole-forbidden transitions of second atom. Another effect corresponds to the scattering situation, when the difference of the excited energies of the two dipole-active transitions of V three level radiator are in the resonance with the dipole-forbidden transitions of the second one. These effects are accompanied with the interferences between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two particle collective decay rate is defined in the description of the atomic correlation functions.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.
The collective decay effects between the dipole-active three-level subsystems in the nonlinear interaction with dipole-forbidden transitions, like 2 S − 1 S of hydrogen-like radiators, are proposed, taking into consideration the cooperative exchanges between two species of atoms through the vacuum field in the scattering and the two-photon resonance processes. One of them corresponds to the situation when the total energy of the emitted two photons by the three-level radiator in the cascade configuration enters into the two-photon resonance with another type of dipole-forbidden transitions of hydrogen-like (or helium-like) atoms. The similar situation appears in the cooperative scattering between two species of quantum emitters when the difference of the excited energies of the two dipole-active transitions of the three-level radiators is in the resonance with the dipole-forbidden transitions of the Hydrogen-like radiators. These effects are accompanied by the interference between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two-particle collective decay rate is defined in the description of the atomic correlation functions taking into consideration the phase retardation between them. The kinetic equations which describe the cooperative processes as the function of time and correlation are obtained. The behavior of the system of radiators at short and long time intervals in comparison with the retardation time between them is studied.
There is an interest in consideration of the propagation of the Gaussian monochromatic light beams through a cell filled with the medium of two-level atoms (in our case, the atomic potassium vapor), which has (at small detuning from resonant transition to low or high frequencies) the refractive index other than unity (n > 1 for v < v01 and n < 1 for v > v01, where v is the light frequency and v01 is the resonant-transition frequency). In this case, the properties of the radiation passed through the cell are changed. In the very close proximity of the resonance, the nonlinear processes (the three-photon electronic stimulated Raman scattering (SRS) and the six-photon parametric scattering (SPS)) play a crucial role. It is precisely these processes in the two-level medium that determine the irreversibly transformed spectral and angular structure of the light beams at the output of the cell.