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arXiv:quant-ph/0206080 · Physical Review A

Spontaneous emission of an atom in front of a mirror

Almut Beige, Jiannis K. Pachos, HERBERT WALTHER

Published Dec 5, 2002• 29 citations
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Abstract

Motivated by a recent experiment [J. Eschner et al., Nature (London) 413, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.

DOI
10.1103/physreva.66.063801

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Motivated by a recent experiment [J. Eschner et al., Nature (London) 413, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.
Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semitransparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.
Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semi-transparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.
The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413,413,413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.
We investigate the spontaneous emission of one atom placed near an oscillating reflecting plate. We consider the atom modeled as a two-level system, interacting with the quantum electromagnetic field in the vacuum state, in the presence of the oscillating mirror. We suppose that the plate oscillates adiabatically, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the time-dependent mode functions, satisfying the boundary conditions at the plate surface, at any given time. Using time-dependent perturbation theory, we evaluate the transition rate to the ground-state of the atom, and show that it depends on the time-dependent atom–plate distance. We also show that the presence of the oscillating mirror significantly affects the physical features of the spontaneous emission of the atom, in particular the spectrum of the emitted radiation. Specifically, we find the appearance of two symmetric lateral peaks in the spectrum, not present in the case of a static mirror, due to the modulated environment. The two lateral peaks are separated from the central peak by the modulation frequency, and we discuss the possibility to observe them with actual experimental techniques of dynamical mirrors and atomic trapping. Our results indicate that a dynamical (i.e., time-modulated) environment can give new possibilities to control and manipulate also other radiative processes of two or more atoms or molecules nearby, for example their cooperative decay or the resonant energy transfer.
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.
The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including the polarization degree of freedom. We look for possible changes in the spontaneous emission rate of the atom resulting from the presence of the parabolic boundary conditions.