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Nonlinear cooperative transfer of atomic energy in the vacuum field of the cavity

Tatiana Pislari

Published Jan 1, 2022• 0 citations
Publisher

Abstract

This paper researches the nonlinear cooperative transfer of atomic energy in the vacuum field of the cavity. Many scientists are concerned about a more detailed study of the cooperation interactions between different subsystems of quantum processes. Based on the theory of resonant interaction with two photons, between two active dipole atoms and a forbidden dipole in resonance with two photons, the author examines for the first time the resonance effect in two ways of the cavity. In some situations, the so-called quantum inseparability needs a new redefinition in order to describe the process that occurs between the photons belonging to these two modes of the cavity. In such a situation, it is better to study the quantum properties of collective modes arising from nonlinear interactions between traditional modes of the electromagnetic field cavity.

DOI
10.52673/18570461.21.3-62.01

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This paper researches the nonlinear cooperative transfer of atomic energy in the vacuum field of the cavity. Many scientists are concerned about a more detailed study of the cooperation interactions between different subsystems of quantum processes. Based on the theory of resonant interaction with two photons, between two active dipole atoms and a forbidden dipole in resonance with two photons, the author examines for the first time the resonance effect in two ways of the cavity. In some situations, the so-called quantum inseparability needs a new redefinition in order to describe the process that occurs between the photons belonging to these two modes of the cavity. In such a situation, it is better to study the quantum properties of collective modes arising from nonlinear interactions between traditional modes of the electromagnetic field cavity.
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.
The cooperative nonlinear scattering processes between two resonator modes stimulated by the excited atomic beam, it is studied. It is demonstrated that these collective scattering phenomena between the Stokes and Anti-Stokes resonator modes take place due to energy transfer between these fields. The quantum proprieties of Stokes and Anti- Stokes fluctuations of the photon numbers have been found. The correlation functions between these fields are expressed through the lasing parameters of the cavity. The experimental scheme of realization of such collective amplification of Stokes (Anti-Stokes) of photon number is proposed.
The paper proposes to unify the two-photon laser and induced cooperative scattering Raman lasing in which the flying ensemble of two-level excited radiators are coupled with the bimodal cavity field in nonlinear two-photon and scattering interactions. It discusses the situation in which the induced two-quantum lasing takes place together with the cooperative scattering conversion of photons between the pump, Stokes, and anti-Stokes cavity modes. The proposed master equation describes cooperative energy exchanges between Raman and two-photon lasing processes by portions of energies multiple to the energy of the entangled photon pair. The generators of such emission and absorption processes belonging to the symmetries of Raman conversion and two-photon cooperative generation are unified. The first symmetry belongs to su(2) algebra connected to the scattering conversion in the Stokes, pump, and anti-Stokes modes of cavity (Opt. Commun.,285(5) (2012) 686–692). The second one belongs to multi-mode su(1,1) symmetry which quantifies the cooperative process belonging to two-photon emission in cavity/fiber mode components of field (see Opt. Commun. 247(4–6) (2005) 381–392). The bimodal collective photon operators are introduced describing the emission or absorption acts of the fixed portion of energy from the cavity equal to the transition energy between the states of each excited atom. A key impact of the study focuses on the statistical properties of the bimodal field and their detection possibilities are proposed for the description of the time evolution of quantum correlations between the field components of Raman conversion and two-photon emission.
The symmetry of the two types of resonances between the spontaneous and induced emissions by two- and single-photon transitions of three inverted radiators from the ensemble is studied. The condition for increasing the collective decay rate of the entangled photon pairs generated by the system relative to the dipole-forbidden transition is found. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enters the two-photon resonance with the dipole-forbidden transitions of the third atom. The second effect corresponds to the scattering situation when the differences of the excited energies of two dipole-active radiators are in resonance with the dipole-forbidden transitions of the third atom. It is shown that transfer of the excited energy between two quantum oscillators off resonance takes place through a dipole-forbidden transition of the thread atom.
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 ignition of two-quantum collective emission of inverted sub-ensemble of radiators due to mutual interaction of this sub-ensemble with other two dipole active atomic subsystems in process of two-photon exchanges between the atoms through the vacuum field is proposed. The three particle resonances between two-photon and single quantum transitions of inverted radiators from the ensemble are proposed for acceleration of collective decay rate of bi-photons, obtained relatively dipole-forbidden transitions of excited atomic sub-ensemble. This mutual interaction between three super-fluorescent processes in subatomic ensembles take place relatively dipole-forbidden transitions in one of radiator subsystem. The collective resonance emission and absorption of two-quanta have nontraditional behavior, accompanied with acceleration and inhibition of collective emission processes of photons.