The photon statistics of spectrum components of the Stokes line in collective Raman scattering are investigated. The cross bunching and cross-antibunching between the spectrum components of the Stokes line and between the Stokes and Rayleigh lines are investigated too.
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.
We develop a Hamiltonian formalism to study energy and position (momentum) correlations between a single Stokes photon and a single material excitation that are created as a pair in the spontaneous Raman scattering process. Our approach allows for intuitive separation of the effects of spectral linewidth, chromatic dispersion, and collection angle on these correlations, and we compare the predictions of the model to experiment. These results have important implications for the use of Raman scattering in quantum protocols that rely on spectrally unentangled photons and collective excitations.