Self-organized formation of atomic coherence via photon exchange in a coupled atom-photon system

The formation of the atomic coherence via a photon field has been considere d to play an essential role in the laser action. The importance of the form ation has been also recognized from the viewpoint of cavity QED. This paper analyzes quantum mechanical dynamics of a self-organized formation of cohe rence between atoms and photon field. We solved an equation of a reduced de nsity operator for a quantum laser model with plural atoms by using coheren t states and orthogonal polynomials, and obtained a solution in a continued fraction form. We numerically evaluate time evolution of averaged physical quantities and quasi-probability density of photon field. Under an appropr iate condition for laser oscillation, time evolution of an average of induc ed atomic dipole moments shows a co-operative phenomenon. Numerical evaluat ion of the quasi-probability density of a photon field reveals that a coher ently more stabilized and stronger photon field emerges as the number of at oms increases. To our knowledge, this is the first detailed quantum mechani cal analysis on the self-organized formation of coherence within atoms beyo nd an intuitive explanation of a laser oscillation. Moreover, our formulati on also provides a tool to analyze phenomena observed in microcavity QED ex periments.