  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.

Quantum Physics;Optics