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Optics Communications

Mutual cooperative effects between the mode components of two-photon and Raman induced cavity lasing processes

N. A. Enaki

Published Jun 11, 2021• 7 citations
Publisher

Abstract

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.

DOI
10.1016/j.optcom.2021.127124

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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 two types of cooperative effects between the converted photons in the multiple steps of Raman lasing are proposed. The first type involves the cooperative process between the photons of one of the steps of Raman conversion. The second cooperative effect appears between the photons belonging to different steps of multiple conversions. This new type of generated coherent state is proposed by novel bimodal entangled sources, which take into consideration both the coherence and collective phenomena between the photons belonging to the system of the bimodal field obtained in multiple Raman emissions. For this, the creation and annihilation operators of the new resonator quasi-particle ware introduced taking into consideration the Hilbert space of field vectors at frequency differences, ωp+1−ωp between the anti-Stokes components of multiple Raman lasing. The application of higher-order multiple Roman bimodal coherent field quantum information is described in accordance with the definition of quantum amplitude and phase of such entangled states of light. The cooperative properties of the bimodal field in the multiple scattering processes of Raman lasing in the cavity/fiber and its interaction with ensemble of atoms prepared in coherent state are proposed. We introduced the new characteristics of bi-modes field in which the multiple Raman scattering takes into consideration the interaction with coherent excitation and non-stationary quantum fluctuations of the generation rate of the introduced quasi particles. Here, we represent the rate moments through the annihilation and generation operators of the cavity quasi-parties.
The cooperative excitation and absorption of light into three cavity modes (pump, Stokes and anti-Stokes), stimulated by excited radiators, is studied as bound entangled states of the photon subsystem. The three modes collective Roman emission and its connection with entangled state is defined introducing the cooperative description between photons of cavity modes. In the case, when the scattering rates in the Stokes and anti-Stokes modes coincide, the SU(2) and SU(1,1) symmetries are applied for a simple description of these cooperative processes. The possibilities to realize this effect in the free space is proposed, replacing the cavity modes with dipole active excited atoms in tow-quantum interaction with dipole-forbidden transitions of D atom. The statistical properties and detection method are proposed using the information entropy and atomic correlation functions.
Abstract The cooperative models of the bimodal field in the multiple quantum scattering nutations are discussed and proposed for possible detections in open cavities. We proposed two types of cooperation between the converted photon processes in these multiple steps of scattering nutation in the cavity. One of them takes into consideration the cooperative process between the photons of each step of the multiple steps of Raman conversion. The second cooperative process takes place between the photons belonging to different steps of multiple scattering conversions. The proposed novel bimodal entangled sources take into consideration both the coherence and collective phenomena between the photons belonging to the system of the bimodal field obtained in multiple scattering emissions. The application of higher-order multiple Raman bimodal coherent field in quantum information is proposed.
Abstract The restoration of the initial state in the Raman interaction of the two atoms with the quantified pump and Stokes (anti-Stokes) cavity modes is analytically obtained. For this the su (2) symmetry representation of the bimodal field and a system of two atoms in scattering interaction is proposed for the simplification of the problem. Using the proprieties of the generators su (2) algebra the exact non-stationary solution of the system of two atoms in interaction with the bimodal field is found, taking into consideration the initial disentangled state between the atomic and field superposition. It is demonstrated that after this collapse and revivals of the inversion of flying atoms in the processes of absorption and emission of the photons from Stokes and pump modes the system atoms and field becomes entangled. The conditions of the restoration of the initial state of the atom-field system were established as a function of the flying time through the resonator possible. A set of discrete flying time intervals for the restoration of the initial disentangled state was found.
The cooperative two-photon 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 propriety of these fields consisted from Stokes and anti-Stokes photon is described by the Master equation. The numerical solution of this equation describes the statistical transformation of n-Stokes photons in anti-Stokes photons.
Abstract The description model of the multiple scattering lasers using the superposition states between the generated photons in the ensemble of bi-modes of the resonator field, we introduced a concept of indistinguishable energy portions generated in the resonator following multiple scattering. Each of these quasi-quanta has energy equal to the difference between the pumping and scattering quantum energies at each step of multiple scattering. The conversion of the photons in the external electromagnetic mode of the resonator destroys this cooperative correlation between the bi-modes and established conservation lows during the cooperative emission. The master equation containing two parameters connected with the gain of quasi-energy portions, and their annihilation due to the losses from the resonator, is proposed. The competition between these two processes is numerically studied. An attractive problem is connected with established quantum correlations between the photons belonging to non-adjacent modes of the cavity. The time behavior of the evolution of correlations between such modes is observed. This conception may be used for the teleportation of information in other modes during the multiple Raman conversion.