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arXiv:quant-ph/0612150

Oscillation structures in the spontaneous emission rate of an atom in a medium with refractive index n between mirrors: a solvable model

Zhao, H. J., M. L. Du

Published Dec 18, 2006• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0612150

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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.
For an atom in a medium with refractive index n sandwiched between two parallel mirrors, we derive an analytical formula for the spontaneous emission rate based on Fermi's golden rule. The oscillations are not transparent in this formula. By performing Fourier transform on scaling variable measuring system size while holding system configuration fixed, we extracted the frequencies of many oscillations in this system. We show that these oscillations correspond to emitted photon closed-orbits going away from and returning to the emitting atom.
For an atom in a medium with refractive index n sandwiched between two parallel mirrors,we derive an analytical formula for the spontaneous emission rate based on Fermi's golden rule.The oscillations are not transparent in this formula.By performing Fourier transform on scaling variable measuring system size while holding system configuration fixed,we extracted the frequencies of many oscillations in this system.We show that these oscillations correspond to emitted photon closed-orbits going away from and returning to the emitting atom,
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.
The spontaneous emission rate of an atom in dielectric slabs is shown to exhibit multiperiodic oscillations when the system scale is varied. These oscillations are calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The extracted frequencies in the emission rates by Fourier transform agree well with actions of short photon closed orbits. The oscillations in the spontaneous emission rates are interpreted as interferences of emitted photon propagating on closed orbits leaving and returning to the emitting atom. This study provides a new understanding of the spontaneous emission process for atoms in the presence of environments.
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.
Quantum electrodynamics formulas are applied to calculate the spontaneous emission rate of an excited atom in the vicinity of a perfect reflecting mirror. The result exhibits that damping oscillating patterns depend sensitively on the distance of the atom to the mirror. And then we use Fourier transform to extract the corresponding frequency of the osciations. In order to explain this phenomena, we are the first to utilize the closed-orbit theory to deal with the spontaneous emission rate of an emitted photon near a mirror. So this study provides a different perspective on the spontaneous emission of atoms in environments.