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理论物理通讯：英文版

Extracting Oscillation Frequencies in Spontaneous Emission Rate of an Atom Between Two Mirrors

Hai Zhao

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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,

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Extracting Oscillation Frequencies in Spontaneous Emission Rate of an Atom Between Two Mirrors

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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.

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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.

Communications in Theoretical Physics•Jan 1, 2010•2 citations
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 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.
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.
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.
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.