Nonperturbative Quantum Theory of Nonlinear Effects in Spontaneous Emission by Two Level Atom Trapped in Damped Nanocavity with a Single Resonance Mode
The nonperturbative theory of the cooperative spontaneous emission from a two level atom trapped in one-dimensional damped nanocavity with a single resonance mode is presented. The time-dependent spectral properties and nonlinear dynamics of a separate photon emission by the micromolecular-like system “excited atom coupled to a resonance decaying mode” have been analyzed. The investigation has been carried out by solving the Schrödinger 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 quantum 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 spectral densities probabilities together with photon emission probability dynamics as functions of time are given for various ratios Г/4g. For Г/4g < 1 the transient emission spectrum reveals the presence of two symmetrical side-bands and the central peak interconnected with each other in the area of interaction with the atom. Since the central component oscillates, decaying simultaneously in time at two rates ∝ Г/2 and ∼ Г/4, in the area of interaction the emission is a triplet with satellites oscillating in the interaction area and being stable outside of it. So the final spectrum is a doublet outside of nanocavity. On the contrary for Г /4g ≥1 the spectrum is a singlet, and the emission occurs in exponentially decaying way.
Keywords: Resonance photon, nanocavity, emission, spontaneous, two level atom.