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Optics Communications

Cooperative scattering effect between Stokes and anti-Stokes field stimulated by a stream of atoms

N. A. Enaki, Marina Ţurcan

Published Nov 29, 2011• 9 citations
Publisher

Abstract

This paper is devoted to the study of the cooperative two-photon scattering processes between two resonator modes stimulated by an excited atomic beam. It has been proved that these collective scattering phenomena between the Stokes and anti-Stokes resonator modes are taking place due to the energy transfer between these fields. The statistical properties of the Stokes and anti-Stokes photons have been described using the photon correlation functions. The numerical solution of this equation describes the statistical transformation of n-Stokes photons into anti-Stokes photons.

DOI
10.1016/j.optcom.2011.11.011

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Soviet Journal of Quantum Electronics•Jun 30, 1977•28 citations
This paper is devoted to the study of the cooperative two-photon scattering processes between two resonator modes stimulated by an excited atomic beam. It has been proved that these collective scattering phenomena between the Stokes and anti-Stokes resonator modes are taking place due to the energy transfer between these fields. The statistical properties of the Stokes and anti-Stokes photons have been described using the photon correlation functions. The numerical solution of this equation describes the statistical transformation of n-Stokes photons into anti-Stokes photons.
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.
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 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.
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.
It is shown that the Stokes and anti-Stokes components, related by the conditions ω s + ω α = 2 ω L and k s + k α =2 k L , are correlated. When the temperature of the scattering material is high [ kT ≫ h ( ω L – ω s )] and/or stimulated scattering exists, this correlation assumes a classical form and is analogous to the Brown-Twiss intensity correlation. This intensity correlation is readily explained by modulation of the pump wave due to molecular vibrations so that the thermal fluctuations of energy of these vibrations are synchronously transferred into the s and α sidebands. At low temperatures and pump intensities (as well as outside Raman resonances) a photon correlation is found which is explained by the simultaneous production of pairs of s and α photons as a result of the spontaneous decay of two pump photons. The statistics of the scattering field in this case assumes a nonclassical form characterized by a relatively high ( m ≫1) probability of pair production compared with the product of the probabilities for the production of separate s and α photons (with the intensity correlation m≤1). An estimate of the rate of coincidences for the scattering of 1-W focused TEM 00 pump radiation in liquid nitrogen yielded ~6 sec –1 and m~10 3 . Analogs of the Kirchhoff equation were obtained for the inelastic scattering of light. These formulas, derived from the conditions of unitarity of the scattering process and equilibrium of matter, define the statistics of the scattered light in terms of the Raman gain and the parametric conversion coefficient.