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Communications in Theoretical Physics

Spontaneous Emission of a Polarized Atom in a Medium Between Two Parallel Mirrors

Wang De-Hua, Huang Kai-Yun, Qiang Xu

Published Jan 1, 2010• 2 citations
Publisher

Abstract

Using the photon closed orbit theory, the spontaneous emission rate of a polarized atom in a medium between two parallel mirrors is derived and calculated. It is found that the spontaneous emission rate of a polarized atom between the mirrors is related to the atomic position and the polarization direction. The results show that in the vicinity of the mirror, the variation of the spontaneous emission rate depends crucially on the atomic polarization direction. With the increase of the polarization angle, the oscillation in the spontaneous emission rate becomes decreased. For the polarization direction parallel to the mirror plane, the oscillation is the greatest; while for the perpendicular polarization direction, the oscillation is nearly vanished. The agreement between our result and the quantum electrodynamics result suggests the correctness of our calculation. This study further verifies that the atomic spontaneous emission process can be effectively controlled by changing the polarization orientation of the atom.

DOI
10.1088/0253-6102/53/1/29

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Using the photon closed orbit theory, the spontaneous emission rate of a polarized atom in a medium between two parallel mirrors is derived and calculated. It is found that the spontaneous emission rate of a polarized atom between the mirrors is related to the atomic position and the polarization direction. The results show that in the vicinity of the mirror, the variation of the spontaneous emission rate depends crucially on the atomic polarization direction. With the increase of the polarization angle, the oscillation in the spontaneous emission rate becomes decreased. For the polarization direction parallel to the mirror plane, the oscillation is the greatest; while for the perpendicular polarization direction, the oscillation is nearly vanished. The agreement between our result and the quantum electrodynamics result suggests the correctness of our calculation. This study further verifies that the atomic spontaneous emission process can be effectively controlled by changing the polarization orientation of the atom.
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.
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,
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.
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 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.