Quantum theory of Stokes-anti-Stokes scattering in a degenerate system in a cavity and vacuum-field Raman splittings

The quantum theory of Stokes-anti-Stokes processes in a degenerate system in a cavity is developed. The Raman transition is pumped by a coherent field. Effects of many atoms, cavity losses, and thermal photons are included in the theory. An exact solution for the model is obtained. An explicit expression for the reduced density matrix of the cavity field is given. The spectrum of the cavity field is obtained and is interpreted in terms of the eigenstates of the effective Hamiltonian describing Stokes-anti-Stokes processes. The spectrum develops sidebands due to strong Raman coupling