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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Spontaneous emission by two initially excited atoms

Kikuo Ujihara, Ho Trung Dung

Published Jan 20, 2003• 0 citations
Publisher

Abstract

We present an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. This analysis applies for two interacting atoms emitting both in a free space and in a cavity structure. In this paper we use the Heisenberg picture. We work under the dipole approximation and the rotating-wave approximation. We assume that all the field modes are initially in the vacuum state and the two atoms A and B are in the upper state. We will concentrate on the motion of the product of the dipole operators of two atoms. Because we have two excitations at t=0, and because we work under rotating-wave approximation, we will always have two excitations, i.e., two excited atoms, or one excited atom plus one photon, or two unexcited atoms with two photons.

DOI
10.1109/cleopr.1999.817880

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We present an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. This analysis applies for two interacting atoms emitting both in a free space and in a cavity structure. In this paper we use the Heisenberg picture. We work under the dipole approximation and the rotating-wave approximation. We assume that all the field modes are initially in the vacuum state and the two atoms A and B are in the upper state. We will concentrate on the motion of the product of the dipole operators of two atoms. Because we have two excitations at t=0, and because we work under rotating-wave approximation, we will always have two excitations, i.e., two excited atoms, or one excited atom plus one photon, or two unexcited atoms with two photons.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
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Summary form only given. We have reported on an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. In this paper we apply this analysis to the two-atom spontaneous emission in a planar microcavity. The two atoms are located on the x-axis on the center plane of a symmetric cavity of length l and are separated by a distance R. The atomic dipoles are oriented in the y-direction parallel to the mirrors. We examine the motion of the probability amplitude of the initial state where both atoms are in the upper state.
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Spontaneous emission in a planar microcavity by two identical and spatially separated two-level atoms, both of them initially excited, is considered under fourth-order perturbation approximation in atom-field coupling constants. A delay-differential equation with proper retardation times for the probability of both atoms in the upper state is derived and expressions for the emitted-light intensity and spectrum are given. It is numerically shown that, while two-atom cooperation is enhanced for small interatomic distances, the two-atom vacuum Rabi oscillation is somewhat suppressed compared to the single-atom oscillation level when the interatomic separation is close to the cavity transverse coherence length.
Spontaneous emission from two systems, namely, NNN identical harmonic oscillators and NNN identical two-level atoms, is studied without the use of the rotating-wave approximation. Certain new features of spontaneous emission, for instance, the dependence of the radiation rate on the initial dipole moment phase, are discussed.