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16th Congress of the International Commission for Optics: Optics as a Key to High Technology

Spontaneous emission by excited two level atom in cavity with zero and non-zero passive linewidth

Vladislav Cheltsov

Published Jul 26, 1993• 0 citations
Publisher

Abstract

The Green function formalism together with the new algorithm in operating with -functions has been used to obtain the 3-peaked spectrum of spontaneous emission of an atom in a weakly damped cavity. The single peaked spectrum and exponential decay law with short (1/Tc) and long (lc/g2) decay times have been shown to exist in the strongly damped cavity.

DOI
10.1117/12.2308459

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 18, 2008•1 citation
The Green function formalism together with the new algorithm in operating with -functions has been used to obtain the 3-peaked spectrum of spontaneous emission of an atom in a weakly damped cavity. The single peaked spectrum and exponential decay law with short (1/Tc) and long (lc/g2) decay times have been shown to exist in the strongly damped cavity.
The time-dependent spectral properties and nonlinear dynamics of a spontaneous photon emitted by two level atom, trapped in damped nanocavity and coupled to a single resonance mode, have been investigated. The results have been obtained with the help of new nonperturbative approach by solving exactly the Schrödinger equation. The theory accounts exactly and simultaneously processes of emission, reabsorptions and leakage of photon. The solution was found with the Green functions formalism, supplemented with the novel algorithm in operating causal singular functions and fundamentals of the theory of quasi-stationary systems. The obtained distributions and emission dynamics are presented with plots as functions of photon frequency detuning and time for various value Γ/4g. For Γ/4g <1 the spectrum is a triplet inside the cavity and doublet outside it. In this case the total emission probability is described by decaying oscillations. For Γ/4g ≥ 1 and Γ/4g >> 1 the spectrum consists of a single central line decaying exponentially with profile depending on value Γ/4g.
Dynamics of the spontaneous emission from a two-level atom embedded in a bisphere microcavity is analyzed theoretically. A bisphere supports a morphology-dependent resonance having such a high quality factor with local field enhancement that the strong coupling between the atom and the cavity can be realized. By taking full account of the photon degree of freedom, we derive theoretically the coupling constant between the atom and the cavity as well as the radiation damping constants, which are used in the conventional cavity QED approach. In addition, we show that the power spectrum of the spontaneous emission at a local observation point is strongly affected by the photon Green function.
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 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 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 Γ/4g of photon escaping rate Γ and coupling constant g are presented. For Γ/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 ∝ Γ/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 Γ/4g ≥ 1 the spectrum is a singlet and the emission occurs in exponentially decaying ways.