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Optica Acta International Journal of Optics

Photon Statistics in Raman Scattering of Intense Coherent Light

Jan Peřina

Published Mar 1, 1981• 22 citations
Publisher

Abstract

The quantum theory of the statistical properties and the photocount statistics of intense radiation in Raman scattering are presented making use of the coherent-state techniques. Both the Heisenberg-Langevin and Fokker-Planck equations approaches are developed. The existence of the conditional Glauber-Sudarshan quasi-distribution is also discussed. The time dependences of the photocount distribution and its factorial moments are demonstrated in the case of stimulated scattering and anticorrelation and antibunching of scattered photons are found.

DOI
10.1080/713820569

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The quantum theory of the statistical properties and the photocount statistics of intense radiation in Raman scattering are presented making use of the coherent-state techniques. Both the Heisenberg-Langevin and Fokker-Planck equations approaches are developed. The existence of the conditional Glauber-Sudarshan quasi-distribution is also discussed. The time dependences of the photocount distribution and its factorial moments are demonstrated in the case of stimulated scattering and anticorrelation and antibunching of scattered photons are found.
The quantum statistical properties of radiation in stimulated Raman scattering are derived including the coupling of Stokes and anti-Stokes modes, in dependence on the frequency mismatch and the mean number of phonons. Making use of the coherent-state technique, the existence of the Glauber-Sudarshan diagonal representation is discussed and the time dependences of the photon statistics are obtained. The anticorrelation and antibunching of scattered photons are found even if there is the frequency mismatch.
Raman scattering from a great number of phonon modes is described from a quantum-statistical point of view within the standing-wave model. The master equation for the completely quantum case, including laser pump depletion and stochastic coupling of Stokes and anti-Stokes modes, is derived and converted to classical equations: either into a generalized Fokker-Planck equation and an equation of motion for the characteristic function or into the master equation in Fock representation. These two approaches are developed both in linear and nonlinear regime. A detailed analysis of scattering into Stokes and anti-Stokes modes in linear regime, i.e., under parametric approximation, is presented. The existence of s-parametrized quasiprobability distributions, in particular the Glauber-Sudarshan P-function, is investigated. An analysis of Raman scattering into separate Stokes and anti-Stokes modes in nonlinear regime, thus including pump depletion, is given. The master equation in Fock representation is solved exactly for the complete density matrix using the Laplace transform method. Short-time solutions, steady-state solutions and approximate compact form solutions are obtained. Relations between the quasidistribution approach based on the Fokker-Planck equation and the density matrix approach based on the master equation in Fock representation are presented. The photocount distribution and its factorial moments as well as variances and extremal variances of quadratures are calculated in both approaches giving the basis for the analysis of the quantum properties of radiation such as sub-Poissonian photon-counting statistics and squeezing. Various statistical moments obtained from numerical calculations utilizing our exact solutions, from the approximate relations for short times, and those obtained under parametric approximation are compared.
The quantum statistical properties of Brillouin scattering of intense laser light are derived including the coupling of Stokes, anti-Stokes and phonon modes, if the anti-Stokes interaction prevails. Making use of the coherent-state technique, the Heisenberg equations of this process are solved neglecting the loss mechanism, and the normal quantum characteristic function and the normal generating function are derived. The time dependences of the photon distribution and its factorial moments are demonstrated if the phonon, Stokes and anti-Stokes modes are initially in a coherent state and periodical anti-bunching of the field is found when the phases of the incident fields fulfil certain phase conditions; the field can also return to the coherent state again.
Photon-photon and photon-phonon anticorrelation effects in Raman scattering are studied theoretically. The Heisenberg equations of motion describing Raman scattering are solved in the short-time approximation. The laser, Stokes, anti-Stokes and phonon modes are quantised. The joint normally ordered characteristic functions are evaluated for modes exhibiting anticorrelation effects. The problem of existence of a Glauber-Sudarshan quasi-distribution function related to anticorrelation effects is considered. The magnitude of the anticorrelation effects depends on the initial statistical properties of the photon and phonon modes.
The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.
Photon statistics of stimulated Raman scattering of squeezed light are considered including additive noise. The phonon system is assumed to be in chaotic or squeezed chaotic states. The influence of nonlinear dynamics is established on the initial non-classical features of light adopting quasi-distribution related to anti-normal ordering, photocount distribution, its factorial moments and principal squeezing parameter. It is shown that the initial non-classical effects are increased by the nonlinear dynamics provided that the Stokes mode is less amplified than the anti-Stokes mode is damped, whereas in the opposite case the non-classical effects are swiftly smoothed out. The frequency detuning can be optimized to have maximum non-classical effects, which can periodically return. However, above a certain bound the non-classical effects are missing with frequency detuning, and also with increasing phonon number, even if the phonon system is squeezed. Small initial squeezing can be increased by the nonlinear dynamics, whereas strong squeezing can only be diminished.