Gain without inversion in three-level V-type system: a dressed-state analysis

A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.