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Optica Acta International Journal of Optics

Photon Correlations in Multi-photon Raman Processes

Przemyslaw Szlachetka, S. Kielich, Jan Peřina, Vlasta Peřinová

Published Dec 1, 1980• 20 citations
Publisher

Abstract

Non-linear interactions between incident and scattered photons (Stokes and anti-Stokes radiation) in Raman and hyper-Raman processes considered as elementary acts, are analysed. Fluctuations of phonons are shown to cause anticorrelation effects between incident and scattered photons. Antibunching of incident laser photons in spontaneous hyper-Raman processes occurs in a similar way to their antibunching in second-harmonic generation.

DOI
10.1080/713820177

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Non-linear interactions between incident and scattered photons (Stokes and anti-Stokes radiation) in Raman and hyper-Raman processes considered as elementary acts, are analysed. Fluctuations of phonons are shown to cause anticorrelation effects between incident and scattered photons. Antibunching of incident laser photons in spontaneous hyper-Raman processes occurs in a similar way to their antibunching in second-harmonic generation.
This paper aims to study the photons antibunching in the fundamental, Stokes and signal modes of CAHRS (coherent anti-Stokes hyper Raman scattering). The generalized interaction Hamiltonian was calculated for different conditions in the Heisenberg picture under short time approximation to observe photons antibunching in the fundamental, Stokes and signal modes of CAHRS. It has been found that antibunching in the fundamental field is dependent upon interaction time, photons number, and coupling strength of field. Third order photon antibunching is found to be nonclassical to a greater extent than second- and first-order photon antibunching for the identical pump photons count. It has been also observed that the effect of photon antibunching in Stokes and signal modes is less prominent than in the fundamental- mode. Furthermore, it is also found that antibunching will increase at short interaction timeswith the increase of depth of nonclassical behavior. Finally, the extent of photons antibunching peaks precisely where the second correlation function is lowest.
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-wave-function formalism provides an alternative description of some quantum optical phenomena in a more intuitive way. We use this formalism to describe the process of correlated Stokes--anti-Stokes Raman scattering. In this process, two photons from a laser beam are inelastically scattered by a phonon created by the first photon (Stokes processes) and annihilated by the second photon (anti-Stokes process), producing a Stokes--anti-Sokes (SaS) photon pair. We arrive at an expression for the two-photon wave function of the scattered SaS photon pair, which is in agreement with a number of experimental results.
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.
It is known that spontaneous Raman scattering is accompanied by the appearance of nonclassical cross correlations of photons at Stokes and anti-Stokes frequencies. Such correlations occur due to the internal nonlinear interaction between electronic and nuclear vibration degrees of freedom. Since the properties of a given media are unchangeable, the possibilities for controlling the cross correlations are limited. This, in turn, restricts the possible applications of the correlated light obtained during the spontaneous Raman scattering. In this work, we investigate the influence of statistical properties of an incident light on the cross correlations of Stokes and anti-Stokes light. We show that the incoherence of the incident light results not only in the incoherence of the scattered light but also in the enhancement of the interbeam coherence at different frequencies. We demonstrate that the cross correlations of Stokes and anti-Stokes light intensities are enhanced when the incident light with high second-order autocorrelation function is applied. Our results pave the way to control correlated light obtained in the process of spontaneous Raman scattering.
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.