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Communications in Theoretical Physics

Correspondence Between Oscillations and Emitted Photon Closed-Orbits in Spontaneous Emission Rate of an Atom Near a Dielectric Slab

Sujun Yun, Fu-He Wang, Yun‐Song Zhou, Du Meng-Li

Published May 1, 2007• 0 citations
Publisher

Abstract

We study the oscillations in the spontaneous emission rate of an atom near a dielectric slab. The emission rate is calculated as a function of system size using quantum electrodynamics. It exhibits multi-periodic oscillations. Four frequencies of the oscillations are extracted by Fourier transforms. They agree with actions of photon closed-orbits going away and returning to the atom. These oscillations are explained as manifestations of quantum interference effects between the emitted photon wave near the atom and the returning photon waves travelling along various closed-orbits.

DOI
10.1088/0253-6102/47/5/024

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We study the oscillations in the spontaneous emission rate of an atom near a dielectric slab. The emission rate is calculated as a function of system size using quantum electrodynamics. It exhibits multi-periodic oscillations. Four frequencies of the oscillations are extracted by Fourier transforms. They agree with actions of photon closed-orbits going away and returning to the atom. These oscillations are explained as manifestations of quantum interference effects between the emitted photon wave near the atom and the returning photon waves travelling along various closed-orbits.
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The formulas of the quantum electrodynamics have been applied to calculate the spontaneous emission rate of excited atom in dielectric microcavity.The results exhibit damping oscillating patterns which depend sensitively on the scaling parameter and geometrical structure.Compared with the case that the emitting atom is immersed in dielectric,the spontaneous emission rate is depressed obviously and the center or the mean value of the oscillations is intimately related to the real refractive index of the local position where the atom is.In order to explain this phenomenon,we utilize the closed-orbit theory to deal with the classical trajectories of the emitted photon,and extract the corresponding frequencies of the oscillations by Fourier transform.It is found that the oscillations can be represented in terms of the closed-orbits of the photon motion constrained in dielectric microcavity,thus providing another perspective on the spontaneous emission of atom sandwiched by dielectric slabs.更多还原
We study the multi-periodic oscillations in the spontaneous emission rate of an atom in a medium with refractive index n sandwiched between two parallel mirrors. The oscillations are not obvious in the analytical formula for the rate derived based on Fermi's golden rule but can be extracted using Fourier transforms by varying the system scale while holding the configuration. The oscillations are interpreted as interferences and correspond to various closed-orbits of the emitted photon going away from and returning to the atom. This system provides a rare example that the oscillations can be explicitly derived by following the emitted wave until it returns to the emitting atom. We demonstrate the summation over a large number of closed-orbits converges to the rate formula of golden rule.
The spontaneous emission rate of two interacting excited atoms near a dielectric interface is studied using the photon closed-orbit theory and the dipole image method. The total emission rate of one atom during the emission process is calculated as a function of the distance between the atom and the interface. The results suggest that the spontaneous emission rate depends not only on the atomic-interface distances, but also on the orientation of the two atomic dipoles and the initial distance between the two atoms. The oscillation in the spontaneous emission rate is caused by the interference between the outgoing electromagnetic wave emitted from one atom and other waves arriving at this atom after traveling along various classical orbits. Each peak in the Fourier transformed spontaneous emission rate corresponds with one action of photon classical orbit.