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Physical Review Letters

Spontaneous Emission from Tunneling Two-Level Atoms

Yonathan Japha, Gershon Kurizki

Published Sep 30, 1996• 19 citations
Publisher

Abstract

We put forward a theory of excitation decay in two-level atoms that tunnel through a square potential barrier while spontaneously emitting photons into an effectively one-dimensional mode continuum. The resulting decoherence can exponentially enhance the total tunneling probability. This enhancement is due to atoms whose final kinetic energy is raised above the barrier by the emission of photons detuned below resonance.

DOI
10.1103/physrevlett.77.2909

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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.
A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).
The long-time behavior of the number of photons in a mode of the electromagnetic field is given in closed form in terms of elementary functions when there is initially one (two-level) atom excited in the presence of NNN unexcited identical atoms and MMM field modes. The radiation trapping which occurs with only one mode disappears when the number of modes MMM approaches the total number of atoms in the continuum mode approximation.
We consider the process of spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap, of width \ensuremath{\Gamma}, the atom emits light during a time interval t\ensuremath{\Gamma}\ensuremath{\ll}1 until the spontaneous emission becomes fully inhibited. We discuss the enhancing of spontaneous emission by tuning the atomic resonance with a one-mode microcavity. In the \ensuremath{\lambda}/4-shifted distributed feedback microcavities which possess the \ensuremath{\delta}-function-like density of states, in the middle of the gap, the process of spontaneous emission has damped Rabi oscillation behavior; the damping depends on the width of the gap and the height of its walls. A profile of the density-of-states gap can be determined from the experimental data on the temporal behavior of the atomic spontaneous decay.