On damping of Rabi oscillations in two-photon Raman excitation in cold $^{87}$Rb atoms

Two-photon Raman excitation between the ground hyperfine states $|5 \ ^2S_{1/2}, F = 2\rangle$ and $|5 \ ^2S_{1/2}, F = 1\rangle$ of $^{87}$Rb atom has been experimentally studied. The Rabi coupling strengths of various transition involved have been calculated in presence of a weak magnetic field. A density matrix formalism has been developed to understand the experimentally observed damping of Rabi oscillations of population in a hyperfine state of $^{87}$Rb atom during interaction with the Raman laser beams. The observed damping of Rabi oscillations has been attributed to the dephasing during the light atom interaction.