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Physica Scripta

Cooperative quantum correlations between Stokes and anti-Stokes modes in four-wave mixing

N. A. Enaki, Marina Ţurcan

Published Mar 1, 2013• 6 citations
Publisher

Abstract

We study the cooperative effects between Raman and hyper-Raman processes in which two quanta from a pumping field are absorbed and another two entangled photons are generated. The symmetries of the involved operators can be reduced to SU(2)-algebra in which the Casimir vector of quasi-momentum of the two fields is conserved. Quantum correlations between the pump and the generated field states are investigated. Cooperative stabilization of two-mode coherent states between Stokes and anti-Stokes photons is shown using both semiclassical and quantum approaches. We show that the relaxation of the system is described by coherent states of the two-mode field. The possibilities of observing cross-correlations between the pump field and the generated field are analyzed.

DOI
10.1088/0031-8949/2013/t153/014021

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We study the cooperative effects between Raman and hyper-Raman processes in which two quanta from a pumping field are absorbed and another two entangled photons are generated. The symmetries of the involved operators can be reduced to SU(2)-algebra in which the Casimir vector of quasi-momentum of the two fields is conserved. Quantum correlations between the pump and the generated field states are investigated. Cooperative stabilization of two-mode coherent states between Stokes and anti-Stokes photons is shown using both semiclassical and quantum approaches. We show that the relaxation of the system is described by coherent states of the two-mode field. The possibilities of observing cross-correlations between the pump field and the generated field are analyzed.
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 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 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.
In this paper we propose the model interaction Hamiltonian which takes in-to consideration the four photon process in interaction of dressed field with 39K atoms. Using the method of elimination of virtual states, we obtain this the effective interaction Hamiltonian which describe the simultaneously generation of photon pairs. The master equation for laser field is obtain, taking into account the good cavity limits in the process of two photon generation. The steady state solution of this equation for threshold case, which takes in to account the quantum fluctuation and photon statistics, is proposed. The cross-correlation function between Stokes and anti-Stokes photon pairs is studied as function of the evolution of the system.
A quantum model of the Raman process with the independent Stokes and anti-Stokes nonlinear interactions is developed to study nonclassical correlations between the photons in the Stokes and anti-Stokes fields. The role of the laser pump amplitude, the ratio of the Stokes and anti-Stokes coupling constants, and the population and losses of the vibrational mode in forming the correlations is elucidated. The g(2){g}^{(2)}g(2) intensity cross-correlation function, noise-reduction factor, two-mode principal squeezing variance, logarithmic negativity, nonclassicality depth, steering parameter, and the Bell parameter are analyzed side by side to shed light to the correlations between the Stokes and anti-Stokes fields. Conditions for having the Stokes and anti-Stokes fields composed of only photon pairs, similarly as it occurs in twin beams in parametric down-conversion, are revealed. They allow for nonzero mean thermal phonon numbers.
We study experimentally nonlinear optical processes in which Stokes and anti-Stokes fields build up under strong, resonant, counterpropagating pump laser excitation in atomic sodium vapor. We find that, at some pump frequency, two off-axis anti-Stokes emissions propagating along reflection-symmetric directions are strongly temporally correlated, with a correlation time of $0.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and a correlation range of 1mrad1\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}1mrad. It is shown by the numerical analysis based on six-wave mixing process involving pump, Stokes, and anti-Stokes waves in the forward and the backward directions that such correlated anti-Stokes emissions are possible when the medium is opaque for the Stokes field and transparent for the anti-Stokes field. Possibilities of quantum correlation for entangled photon generation using this system are discussed.