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Chinese Physics Letters

Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

Li Cheng-Gai, Hongwei Yu

Published May 1, 2009• 1 citation
Publisher

Abstract

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom's distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z 4 when the atom's distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z 3 when z is very small.

DOI
10.1088/0256-307x/26/5/050401

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We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom's distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z 4 when the atom's distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z 3 when z is very small.
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We consider an inertial two-level atom in interaction with a real massless scalar quantum field in a spacetime between two parallel reflecting plane boundaries, and calculate the contributions of vacuum fluctuations and radiation reaction to the rate of change of the atomic energy. Our results show that there exists a regime of the separation L between the two boundaries such that the excited atom's spontaneous emission is impossible. There also exist certain values of the atom's position such that the corrections due to the presence of boundaries balance each other, so that the atom's spontaneous emission rate is the same as if there were no boundaries at all.
We discuss the radiative level shifts of a uniformly accelerated atom moving between two infinite reflecting plates and interacting with a massless scalar field in the vacuum state. The atom, supposed to be a two-level system, accelerates in a direction parallel to the conducting plates. We evaluate separately the contributions of vacuum fluctuations and radiation reaction field to the energy shift of the atomic levels, and discuss their dependence on acceleration, atomic position and cavity length.
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We study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.
We calculate the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy for a multi-level hydrogen atom in the multipolar coupling scheme in a spacetime with a reflecting boundary. Our results show that, due to the presence of the boundary, the polarizations of the atom in the parallel direction and in the normal direction are weighted differently in terms of their contributions to the spontaneous emission rate, which is an oscillating function of the atom distance from the boundary. The possible experimental implications of our result are briefly discussed.