Self-Organized Formation of Atomic Coherence via Photon Exchange in a Coupled Atom-Photon System
Chikako Uchiyama, Fumiaki Shibata · Journal of the Physical Society of Japan · 2000
The formation of the atomic coherence via a photon field has been considered to play an essential role in the laser action. The importance of the formation has been also recognized from the viewpoint of cavity QED. This paper analyzes quantum mechanical dynamics of a self-organized formation of coherence between atoms and photon field. We solved an equation of a reduced density operator for a quantum laser model with plural atoms by using coherent 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 appropriate condition for laser oscillation, time evolution of an average of induced atomic dipole moments shows a co-operative phenomenon. Numerical evaluation of the quasi-probability density of a photon field reveals that a coherently more stabilized and stronger photon field emerges as the number of atoms increases. To our knowledge, this is the first detailed quantum mechanical analysis on the self-organized formation of coherence within atoms beyond an intuitive explanation of a laser oscillation. Moreover, our formulation also provides a tool to analyze phenomena observed in microcavity QED experiments.