lasers without inversion: density operator method

a quantum theory of a two and three-level laser with injected atomic coherence is developed by using a density operator method, to the best of our knowledge, for the first time. the initial atomic coherence plays an essential role. at steady state, the equation of motion for the density operator yields to exhibit laser without inversion and a phase locking but no threshold for the laser field. the fokker-planck equation is also derived for three level lasers and the laser action is analyzed in terms of the coefficients of this equation which results in the quantum noise quenching. one of the most important aspects of our method is its capability to analyze the coherently pumped laser action in n-level systems in a simple fashion