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Optica Acta International Journal of Optics

Quantum Statistics of Stimulated Raman Effect in a Gaseous System

B. K. Mohanty, N. Nayak, Partha Sarathi Gupta

Published Aug 1, 1982• 6 citations
Publisher

Abstract

A quantum mechanical treatment of stimulated Raman effect in a gaseous system is presented. The atomic system is described by a two-level system. The radiation fields also obey the laws of quantum mechanics. The effects of atomic motion and the detuning in one-photon absorption and two-photon emission are incorporated in the analysis. The equation of motion describing the photon-statistics of all the fields are obtained. As a special case, the time evolution of the average photon number, second order coherence and output variance of the Stokes field is studied. The results show a non-linear dependence on the parameters representing atomic motion, detuning and atomic relaxation constants.

DOI
10.1080/713820955

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A quantum mechanical treatment of stimulated Raman effect in a gaseous system is presented. The atomic system is described by a two-level system. The radiation fields also obey the laws of quantum mechanics. The effects of atomic motion and the detuning in one-photon absorption and two-photon emission are incorporated in the analysis. The equation of motion describing the photon-statistics of all the fields are obtained. As a special case, the time evolution of the average photon number, second order coherence and output variance of the Stokes field is studied. The results show a non-linear dependence on the parameters representing atomic motion, detuning and atomic relaxation constants.
We present a theoretical treatment for third-harmonic generation in gaseous systems by describing the atomic system as well as the radiation field quantum mechanically. The atomic system is represented by two energy levels. The effects of detuning in the two-photon interactions and the atomic motion on the third-harmonic generation are taken into account. The photon statistics of the third-harmonic field are obtained. The average photon number, second-order coherence, and output variance of the third-harmonic field are discussed. The above results show a nonlinear dependence on the detuning in the two-photon interactions and the Doppler parameter.
A fully quantum mechanical density matrix formalism of stimulated hyper-Raman scattering in an inhomogeneously broadened system is presented including the effects of detuning, higher order non-linearities and loss. The equations are solved to fourth-order in the atom-field coupling constant under a situation of low loss, and Stokes-photon statistics are studied in the steady state. The coherence properties of the Stokes beam are found to increase with increasing amplification factor and with decreasing detuning. The occurrence of anti-bunching phenomena is investigated.
Second-harmonic generation in a degenerate two-level gaseous system is considered with atomic motion taken into account. The diagonal elements of the dipole matrix are assumed to be present. We find the photon statistics of the second-harmonic field to be considerably influenced by the detuning in the two-photon absorption. The threshold condition is discussed. We obtain the average second-harmonic photon number and thus calculate the dimensionless intensity parameter. The output variance of the second-harmonic field is discussed.
The nonlinear process of the stimulated Raman effect is treated theoretically. Simple expressions are derived for the initial rates of change and limiting steady state values of the first two moments, the degrees of second-order coherence and the correlation function of the pump and Stokes beams. An analytical solution for the time dependence of the joint photon probability distribution of the two light beams is obtained and then employed to calculate some numerical results for various special cases of interest, and the significance of these results is discussed in physical terms. Simpler approximate expressions are also derived for the case where the pump beam is much more intense than the Stokes beam.
The process of stimulated Raman scattering is described by the model of 2D oscillator. The photons of Stokes mode are described by one mode of the oscillator and phonons of the medium are described by the other mode of oscillator. The interaction of photons and phonons is taken to be quadratic in the creation and annihilation operators of the photons and phonons. New time-dependent integrals of motion are found for stimulated Raman scattering within the framework of this model. The photon-phonon probability-distribution function is found in terms of Hermite polynomials of four variables. It is shown that the squeezing phenomenon can be transferred from one mode to the other due to interaction. The statistical dependence appears due to interaction as well. An explicit formula of the photon-number probability distribution as a function of the laser-field intensity and the medium parameters is obtained both in terms of Hermite polynomials of two variables and in terms of Legendre polynomials after the averaging of the photon-phonon probability-distribution function over the phonon mode. The mean photon number and its dispersion in the Stokes mode are expressed as functions of the medium parameters and a parameter of the interaction. It is shown that if the medium is initially prepared, then after the interaction with laser field the photons are created in squeezed state. The classical propagator for stimulated Raman scattering is found within the framework of the symplectic tomography scheme.
A simple description of the stimulated Raman emission of Stokes radiation, and of the induced absorption found by Stoicheff at the anti-Stokes frequency, is based on the semiclassical theory of radiation. This theory gives the well-known formulas for absorption and stimulated emission when carried to the first order in the time-dependent perturbation due to the interaction of the light beam with the molecules. If there are two light beams of frequencies ωL and ω, the second-order perturbation may be associated with stimulated emission at the Stokes frequency ω=ω−1=ωL—ωR and with induced absorption at the anti-Stokes frequency ω=ω1=ωL+ωR, where ωL is the laser frequency and ωR a Raman-active vibrational frequency; in both cases, there is a molecular transition to the excited vibrational state. The highly directional and very sharp anti-Stokes emission at ω1 arises from the conversion by molecules in intense beams at ωL and ω−1 of two ωL photons into an ω−1, ω1 pair. Like spontaneous emission from excited states, the production of this anti-Stokes radiation requires the full quantum theory of radiation for an adequate description. The emission of ω1 and the observed directional absorption of ω−1 due to the reverse conversion ω−1+ω1→2ωL are explained. The anti-Stokes emission is proportional to the Stokes intensity and to the square of that of the laser, and to the square of the molecular number density; its sharpness is due to the absence of a molecular transition. The generation of photon pairs ω−n+ωn, where ωn=ωL+nωR, can occur for all values of n, but it is most efficient for n=1, due to resonance in the appropriate molecular hyperpolarizability and to the intensity of the Stokes beam at ω−1.