Single-photon emission via Raman scattering from the levels with partially resolved hyperfine structure

The probability of emission of a single-photon via Raman scattering of laser pulse on the three-level Λ - type atom in microcavity is studied. The duration of the pulse is considered to be short enough, so that the hyperfine structure of the upper level remains totally unresolved, while that of the lower level is totally resolved. The coherent laser pulse is assumed to be in resonance with the transition between one hyperfine-structure component of the lower atomic level and all hyperfine-structure components of the upper level, while the quantized cavity field is assumed to be in resonance with the transition between the other hyperfine-structure component of the lower level and all components of the upper one. The dependence of the photon emission probability on the mutual orientation of polarization vectors of the cavity mode and of the coherent laser pulse is analyzed. Particularly, the case is investigated, when the total electronic angular momentum of the lower atomic level equals 1/2, which is true for the ground states of alkali atoms employed in the experiments on deterministic single-photon emission. It is shown, that in this case the probability of photon emission equals zero for collinear polarizations of the photon and of the laser pulse, and the probability obtains its maximum value, when the angle between their polarizations equals 60°.