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arXiv:quant-ph/9711071 · Journal of Physics B Atomic Molecular and Optical Physics

Boundary effects influencing single-atom spontaneous emission in a linear atomic chain

Konstantin V Krutitsky, Jürgen Audretsch

Published Jun 14, 1998• 2 citations
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Abstract

As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain.

DOI
10.1088/0953-4075/31/11/022

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As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain.
Boundary problem of quantum optics for spontaneous emission of atom embedded in one-dimensional chain of discrete dipoles is solved. The role of boundary effects caused by violation of translational symmetry in atomic spatial distribution is investigated. Life time of excited state and frequency shift of atomic transition are calculated. It is shown that these spectral characteristics significantly depend on atomic position in the chain. Angular distribution of spontaneous photons is also investigated. Theoretical analysis is based on the system of Heisenberg equations for atomic and field operators. For the calculation of the mode functions it is employed as the method of integro-differential equations.
We have theoretically investigated the process of spontaneous emission of initially excited two-level atom inside and outside of ultra-thin dielectric film. Dielectric medium is considered as discrete-continuous system of interacting dipoles. For the solution of this boundary problem of quantum optics we use Heisenberg equations for atomic operators. Mode functions of ultra-thin film are calculated by direct solution of integro-differential field equation. Coordinate dependences of excited state life time are analyzed and it is shown that consideration of near-field effect may essentially change spectral properties of the atoms located at small distances from the surface.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.
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.
We investigate the dynamical properties of the radiation field emitted from an excited two-level atom in a photonic crystal. If the transition frequency of the atom lies within a certain frequency range above the band edge, the emitted field consists of two components that show a different decay dynamics. In particular it is shown that one field component decreases faster than the atomic population with a decay constant depending on the distance from the atom. As a consequence, the decay rate of the electromagnetic field is spatially varying and, in general, can not be identified with the corresponding rate for the atomic population.
It is a well known fact that the presence of material bodies in the vicinity of an atom affects its interaction with the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous-emission rate of a given excited atom is altered when this atom is placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism upon which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom, but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. The oscillatory pattern for the spontaneous-emission rate of the atom as we vary its relative position to the wedge as well as the phenomenon of suppression are shown by a few graphs.