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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum coherence and squeezing in stimulated Raman scattering

Joseph W. Haus, Kee Choon Yeong, Alexei Vladimirovich Chizhov

Published May 10, 1996• 0 citations
Publisher

Abstract

Two models are considered to examine quantum correlations between the Stokes and anti- Stokes fields generated in stimulated Raman processes; the first is a cavity model and the second treats propagating fields. The coherence introduced through the dynamics evolution are manifest through their higher-order correlation functions where sum-squeezed states are identified.

DOI
10.1117/12.239680

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Two models are considered to examine quantum correlations between the Stokes and anti- Stokes fields generated in stimulated Raman processes; the first is a cavity model and the second treats propagating fields. The coherence introduced through the dynamics evolution are manifest through their higher-order correlation functions where sum-squeezed states are identified.
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 non-classical effects of squeezing of light in coherent anti-Stokes Raman scattering (CARS) and coherent anti-Stokes hyper-Raman scattering (CAHRS) are investigated under the short-time approximation based on a fully quantum mechanical approach. In an idealized model CARS, the interaction is looked upon as a process involving absorption of a pump photon and emission of a Stokes photon, which is followed by absorption of a pump photon and subsequently emission of an anti-Stokes photon at a different frequency, whereas CAHRS is looked upon as a process involving absorption of two pump photons and emission of a Stokes photon, which is followed by absorption of two more pump photons and subsequent emission of an anti-Stokes photon at a different frequency. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. It is shown that squeezing in the Stokes and anti-Stokes mode in CARS is found to be dependent on amplitude-squared squeezing of the initial pump field while, in CAHRS, it is dependent on the fourth-order amplitude squeezing of the initial pump field. Higher-order squeezing can be converted to linear squeezing through these processes. It is also shown that squeezing is greater in CAHRS than the corresponding squeezing in CARS.
We consider a cavity model in which the dynamics of photons and phonon modes, as well as their interaction with a boson reservoir, are taken into account. The second- and fourth-order quantum coherence functions are evaluated and examined under various conditions of coupling coefficients, phases, and noise. For the case when the laser–anti-Stokes coupling is larger than the laser–Stokes coupling, the quantum correlations between field operators are identified in the form of sum and ordinary squeezing. The reservoir can be noisy without severely degrading the sum squeezing.
We develop the quantum theory of stimulated hyper-Raman scattering (HRS) and discuss the quantum statistics of pump and Stokes fields. We show that the initially coherent pump field acquires a strong squeezing that exceeds the similar squeezing in other nonlinear processes also involving two-photon absorption. Stokes field statistics are analysed in detail as a function of the initial statistics of both modes. Bunching effects are shown to be amplified in the short-time region, while in asymptotics the antibunching of Stokes photons becomes dominant, which in many cases results in sub-Poissonian statistics of Stokes mode. We also find a number of correlation effects between the photons of the two modes.
Coherent light coupled to a third-order nonlinear medium is responsible for spontaneous and for stimulated Raman processes. The analytical solutions up to second order in coupling constants of various field modes for spontaneous Raman and for stimulated Raman processes are utilized to obtain the amplitude-squared and amplitude-cubed squeezing of the input coherent light. The amplitude-squared and amplitude-cubed squeezing are completely ruled out for all modes for spontaneous Raman processes. For stimulated Raman processes, we observe that the squeezing for amplitude-squared and amplitude-cubed are possible for pump and for vibrational phonon modes. It is found that the percentage of higher ordered amplitude squeezing decreases with the increase of the orders. The squeezing in Stokes and in anti-Stokes modes are ruled out even for stimulated Raman processes.