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Physics of Particles and Nuclei Letters

Stokes-anti-Stokes entanglement in stimulated Raman scattering

Alexei Vladimirovich Chizhov

Published Nov 1, 2009• 1 citation
Publisher

Abstract

A cavity model of Raman scattering from phonons by an undepleted laser field is considered. The fields in the interaction are coupled to the boson reservoir that produces the damping mechanism in the model. An analysis for the origination of quantum entanglement between the Stokes and anti-Stokes fields, depending on their coupling constants with the reservoir bosons and on the state of the reservoir, is performed under the assumption of the initial coherent state of phonons.

DOI
10.1134/s1547477109060120

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A cavity model of Raman scattering from phonons by an undepleted laser field is considered. The fields in the interaction are coupled to the boson reservoir that produces the damping mechanism in the model. An analysis for the origination of quantum entanglement between the Stokes and anti-Stokes fields, depending on their coupling constants with the reservoir bosons and on the state of the reservoir, is performed under the assumption of the initial coherent state of phonons.
In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.
We investigate the dynamics of a two-mode stimulated Raman scattering model including propagation and the quantum correlations that develop between the Stokes and anti-Stokes fields. For example, under certain conditions two-mode squeezed states can result. We report results for quadrature squeezing and sum squeezing. Quadrature squeezing only occurs when the anti-Stokes coupling constant is larger than the Stokes coupling constant. The amount of squeezing increases as the damping of the material polarization is increased. \textcopyright{} 1996 The American Physical Society.
The operator solution of a completely quantum mechanical Hamiltonian of the Raman processes is used here to investigate the possibility of obtaining intermodal entanglement between different modes involved in the Raman processes [e.g., pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode]. Intermodal entanglement is reported between (a) pump mode and anti-Stokes mode, (b) pump mode and vibration (phonon) mode, (c) Stokes mode and vibration phonon mode, and (d) Stokes mode and anti-Stokes mode in the stimulated Raman processes for variation of the phase angle of complex eigenvalue ${\ensuremath{\alpha}}_{1}$ of pump mode aaa. Some incidents of intermodal entanglement in the spontaneous and the partially spontaneous Raman processes are also reported. Further, it is shown that the specific choice of coupling constants may produce genuine entanglement among Stokes mode, anti-Stokes mode, and vibration-phonon mode. It is also shown that the two-mode entanglement not identified by Duan's criterion may be identified by Hillery-Zubairy criteria. It is further shown that intermodal entanglement, intermodal antibunching, and intermodal squeezing are independent phenomena.
A quantum-mechanical model of Raman scattering from a phonon bath is formulated. A master equation is derived for the density operator of the light fields alone. This model correctly describes the stochastic coupling of Stokes and anti-Stokes radiation through the phonon bath. Since quantum fluctuations are included, this treatment contains the spontaneous and stimulated Raman effects in one self-consistent formalism. The photon statistics of the light fields are obtained by the solution of a Fokker-Planck equation.