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

Role of symmetric and antisymmetric states in spontaneous emission by two initially excited atoms

Kikuo Ujihara

Published Nov 13, 2002• 0 citations
Publisher

Abstract

An analysis for investigation of the role of symmetric and antisymmetric states in cooperative spontaneous emission by two initially excited atoms is presented taking into account the finite photon transit time between the atoms. The iterative calculation can go beyond the Markov approximation.
DOI
10.1109/cleopr.2001.968022

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The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.
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.
Collective effects in the spontaneous emission pattern of two identical two-level atoms a fixed distance apart and sharing initially a single excitation are investigated. It is shown that the interference can take place even when it is known for certain which atom is excited initially. This interference is due solely to the atomic coherence established through multiple photon absorptions and reemissions and will disappear if it is ignored. The interference patterns with and without collective effects are compared for symmetric and antisymmetric initial states. The dark center from an antisymmetric state is shown both analytically and numerically.
This paer is concerned with the spontaneous-emision rate of two two-level atoms which have different resonance frequencies and whose spatial separation is much smaller than the corresponding mean resonance wavelength. The total radiation rate of such an atom pair is calculated completely quantum mechanically as a function of time. Explicit results are given for various values of the frequeny difference and the following initial states of the atomic system: (a) both atoms in the excited state, (b) one taom in the excited state the other in the ground state, (c) a symmetric combination of those states, (d) an antisymmetric combination of those states, and product states where each atom is in an equal superposition of its ground and excited states, for which the expectation values of the dipole moments are nonzero and may be considered to be osicillating (e) in phase, (f) in opposite phae, and (g) in random phase. Oscillations are found to appear in the radiation rate in all cases when the frequency difference becomes larger than a certain critical value, viz., the mean half-width of the atomic resonance lines. The oscillations are especially pronounced for the initial atomic states (c), (d), (e), and (f), which exhibit superradiance and radiation trapping. For example, for atoms in the antisymmetric state (d), for which the radiation from two identical atoms is zero (completely self-trapped), a pair of nonidentical atoms begins radiating and even oscillates into the superradiant region at times.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
In this paper, we study cooperative two-photon transitions in a system of two (nonoverlapping) atoms for two processes: two-photon spontaneous emission and two-photon resonance fluorescence. Expressions are obtained for the energy shifts and decay rates due to the interaction of the atoms with and via the field. The altered decay rates signal the existence of superradiance and subradiance in the two-atom system. The energy shifts of the single-excitation states are found to be proportional to ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$ for small atomic separations R, and to ${\mathit{R}}^{\mathrm{\ensuremath{-}}2}$ for large separations.