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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Short-time squeezing in spontaneous Raman and stimulated Raman scattering

Ashok Kumar, Partha Sarathi Gupta

Published Oct 1, 1995• 37 citations
Publisher

Abstract

The non-classical effect of squeezing of light in spontaneous Raman and stimulated Raman processes are investigated under a short-time approximation based on a fully quantum mechanical approach. A Raman process is looked upon as a two-photon and one-phonon interaction process. Squeezing in amplitude, amplitude squared and amplitude cubed have been investigated. The occurrence of squeezing is observed in the fundamental mode in spontaneous Raman and stimulated Raman scattering. The squeezing in a Stokes field is found to be dependent on squeezing of the initial pump field.

DOI
10.1088/1355-5111/7/5/005

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The occurrence of fourth and fifth-order squeezing in the fundamental mode of the electromagnetic field in spontaneous and stimulated Raman processes under the short-time approximation is investigated on the basis of a fully quantum-mechanical approach. In an idealized model, the Raman process is looked upon as a two-photon on a one phonon interaction process. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The dependence of fourth- and fifth-order squeezing in terms of the signal-to-noise ratio on the number of photons is investigated. We have also established the amplitude squeezing effects in the Stokes and vibrational modes, which is found to be dependent on higher-order difference squeezing showing a difference squeezing that can be converted to normal squeezing.
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Squeezing of the electromagnetic field is investigated in the pump, Stokes and parametric mode in spontaneous and stimulated four-wave mixing processes under a short-time approximation based on a fully quantum mechanical approach. The occurrence of squeezing in amplitude and amplitude squared of the fundamental mode has been investigated. The dependence of squeezing on the photon number is noticed and the degree of squeezing in the first and second-order is also investigated. Squeezing occurs in the fundamental mode in both spontaneous and stimulated processes, whereas squeezing in the Stokes and parametric modes is found to be dependent on squeezing of the initial pump field.
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.
Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.