Spectral properties and nonlinear dynamics of a spontaneous photon emitted by two level atom trapped in a damped nanocavity with a single resonance mode

The nonperturbative theory of the cooperative spontaneous emission from a two level atom trapped in one-dimentional damped nanocavity with a single resonance mode is presented. The time-dependent spectral properties and nonlinear dynamics of a separate photon emission by the micro-molecular-like system "excited atom coupled to a resonance decaying mode" have been analyzed. The investigation has been carried out by solving the Schrodinger equation in the interaction picture with the help of the Green functions method in the Heitler-Ma's form. The formalism was supplemented with the novel algorithm in operating causal singular functions and with fundamentals of the theory of quasi-stationary systems. The proposed theory accounts automatically of both reabsorptions of emitted photon and its simultaneous escaping out of the cavity. Solutions of the wave equation were found without using intermediate virtual states and series expansions. In accordance with the theory of quasi-stationary systems the field of mode decaying exponentially in the empty nanocavity was represented with the Lorenz-shaped packet of stationary photonic states (quasi-modes). The electro-dipolar interaction between the atom and the mode field was adopted to be switched on suddenly. The expressions and plots of emission probabilities spectral densities together with photon emission probability dynamics as functions of time for various ratios Gamma/4g of photon escaping rate Gamma and coupling constant g are presented. For Gamma/4g <1 the transient emission spectrum reveals the presence of two symmetrical side-bands and of the central peak, the latter decaying in time at the rate proportional to Gamma/2 so that the final spectrum is a doublet. In this case the photon emission probability is described by decaying oscillations. On the contrary for Gamma/4g >= 1 the spectru. in is a singlet and the emission occurs in exponentially decaying way.