Spontaneous emission from the bare ground state of an optically driven three-level atom: Perturbation theory and energy conservation

We present a perturbative derivation of the fluorescence spectrum for a three-level atom driven by a classical radiation field. The energies of the three atomic levels are equal to HBAR omega(i) (i=1, 2, and 3) with omega(3)>omega(2)>omega(1) and omega(32)much greater than omega(21) (omega(ij)=omega(i)-omega(j)). The radiation field, having a frequency Omega>omega(31), can be considered to drive the 2-3 transition only. Spontaneous emission from the ground state, via a normally counter-rotating atom-vacuum interaction term in the Hamiltonian, conserves energy when a photon is subsequently absorbed from the laser field. The spectrum is explained in terms of a Raman process, and in terms of an interaction between the laser field and the coupled atom-vacuum field system. Connection is made with a dressed-atom description of the problem.