It is shown that the Stokes and anti-Stokes components, related by the conditions ω s + ω α = 2 ω L and k s + k α =2 k L , are correlated. When the temperature of the scattering material is high [ kT ≫ h ( ω L – ω s )] and/or stimulated scattering exists, this correlation assumes a classical form and is analogous to the Brown-Twiss intensity correlation. This intensity correlation is readily explained by modulation of the pump wave due to molecular vibrations so that the thermal fluctuations of energy of these vibrations are synchronously transferred into the s and α sidebands. At low temperatures and pump intensities (as well as outside Raman resonances) a photon correlation is found which is explained by the simultaneous production of pairs of s and α photons as a result of the spontaneous decay of two pump photons. The statistics of the scattering field in this case assumes a nonclassical form characterized by a relatively high ( m ≫1) probability of pair production compared with the product of the probabilities for the production of separate s and α photons (with the intensity correlation m≤1). An estimate of the rate of coincidences for the scattering of 1-W focused TEM 00 pump radiation in liquid nitrogen yielded ~6 sec –1 and m~10 3 . Analogs of the Kirchhoff equation were obtained for the inelastic scattering of light. These formulas, derived from the conditions of unitarity of the scattering process and equilibrium of matter, define the statistics of the scattered light in terms of the Raman gain and the parametric conversion coefficient.
It is shown that the Stokes and anti-Stokes components, related by the conditions ω s + ω α = 2 ω L and k s + k α =2 k L , are correlated. When the temperature of the scattering material is high [ kT ≫ h ( ω L – ω s )] and/or stimulated scattering exists, this correlation assumes a classical form and is analogous to the Brown-Twiss intensity correlation. This intensity correlation is readily explained by modulation of the pump wave due to molecular vibrations so that the thermal fluctuations of energy of these vibrations are synchronously transferred into the s and α sidebands. At low temperatures and pump intensities (as well as outside Raman resonances) a photon correlation is found which is explained by the simultaneous production of pairs of s and α photons as a result of the spontaneous decay of two pump photons. The statistics of the scattering field in this case assumes a nonclassical form characterized by a relatively high ( m ≫1) probability of pair production compared with the product of the probabilities for the production of separate s and α photons (with the intensity correlation m≤1). An estimate of the rate of coincidences for the scattering of 1-W focused TEM 00 pump radiation in liquid nitrogen yielded 6 sec –1 and m10 3 . Analogs of the Kirchhoff equation were obtained for the inelastic scattering of light. These formulas, derived from the conditions of unitarity of the scattering process and equilibrium of matter, define the statistics of the scattered light in terms of the Raman gain and the parametric conversion coefficient.
A quantum model of the Raman process with the independent Stokes and anti-Stokes nonlinear interactions is developed to study nonclassical correlations between the photons in the Stokes and anti-Stokes fields. The role of the laser pump amplitude, the ratio of the Stokes and anti-Stokes coupling constants, and the population and losses of the vibrational mode in forming the correlations is elucidated. The g(2) intensity cross-correlation function, noise-reduction factor, two-mode principal squeezing variance, logarithmic negativity, nonclassicality depth, steering parameter, and the Bell parameter are analyzed side by side to shed light to the correlations between the Stokes and anti-Stokes fields. Conditions for having the Stokes and anti-Stokes fields composed of only photon pairs, similarly as it occurs in twin beams in parametric down-conversion, are revealed. They allow for nonzero mean thermal phonon numbers.
The correlated Raman scattering, referred to here as the SaS process, occurs with the annihilation, within a material, of two photons of an excitation laser and the creation of a quantum correlated Stokes (S) and anti-Soktes (aS) photon pair where the phonon created in the S process is annihilated in the aS scattering. We found that, in addition to real SaS process where the energy exchange coincides with the energy of a vibrational state of the material, there is also the virtual SaS process, whose the exchange of energy and momentum between the photons of the laser, generating the S-aS photon pair, is mediated by a virtual vibrational excitation, setting up a photon-photon interaction similar to the electron-electron attraction responsible for the creation of Cooper pairs of the BCS theory of superconductivity. We observed the SaS process in transparent media in general, by measuring non-classical values of the normalized second-order cross-correlation function of the Stokes and anti-Stokes fields, 2(0). In diamond, we characterize the intensity of the virtual SaS scattering ( ) as a function of the virtual phonon energy, proving that the SaS process occurs only when the photon-photon interaction is attractive, as in the BCS theory for the Cooper pairs. We show that photons S and aS from the SaS process are scattered predominantly in the same polarization as the excitation laser of the sample and, with this, we implemented the pump-probe technique to study the lifetime of the real phonon (obtained in the diamond order 2.8 ps ) and the lifetime of the virtual excitation, which proved to be inferior to the temporal resolution of the measurement’s, characterizing one of the main differences between the two processes. We also observed that, due to the relations of energy and momentum conservation, have the same spatial intensity profile of the non-interacting laser that crosses the sample, different from the behavior observed for uncorrelated Raman scattering which spreads photons in all directions. We observed that the efficiency of the SaS scattering is proportional to the Raman scattering cross-section when we compare the process in different hydrocarbons and we generalize the observations made in the diamond to the sample of liquid decane. In water, the values of 2(0), predicted by the theoretical description of the process, corroborate the experimental data, validating the BCS theory for virtual SaS scattering, setting the pair of Stokes and anti-Stokes photons as counterparts of the Cooper pairs.
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.
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.
The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1
The Raman effect is the inelastic scattering of photons by matter. When a monochromatic light beam (pump beam) propagates in an optical fibre, spon- taneous Raman scattering transfers some of the photons to new frequencies. The probability of a photon scattering to a particular frequency shift, depends on that frequency shift, forming a characteristic spectrum. The scattered photons may lose energy (Stokes) or gain energy (anti-Stokes). If the pump beam is linearly polarized, then the polarization of scattered photons may be the same (parallel scattering) or orthogonal (perpendicular scattering). If photons are already present at other frequencies then the probability of scattering to those frequencies is enhanced (stimulated scattering). In this thesis, the equations governing the Raman effect, both in bulk glass and single mode fibre, are restated. The probability of spontaneous scattering (parallel and perpendicular) in an optical fibre has been measured for frequency shifts between 4THz and 58THz. Particular attention has been given to those frequency shifts where the scattering is intrinsically weak. This has identified those frequency shifts where it might be possible to eliminate Raman noise from experiments designed to generate quantum states of light in optical fibres using four wave mixing. From the measured scattering probabilities, the Raman equations can be used to predict the scattering cross-section in bulk glass. The prediction is found to be in reasonable agreement with measurements of the bulk glass cross-section published by other authors. By increasing the pump power, the transition to stimulated scattering has been observed. In the case of Stokes scattering there is reasonable agreement between the Raman equations and experimental observations. In the case of anti-Stokes scattering, and in the limit of very high pump power, behaviour is observed which is not predicted by the Raman equations, indicating that other processes must be included to successfully describe such experiments.