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arXiv:1412.1655 · EPJ Web of Conferences

Spontaneous Photon Emission in Cavities

G. Alber, N. Griebe

Published Jan 1, 2014• 1 citation
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Abstract

We investigate spontaneous photon emission processes of two-level atoms in parabolic and ellipsoidal cavities thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms and the energy density of the resulting few-photon electromagnetic radiation field by using semiclassical methods for the description of the multimode scenario. Based on this approach photon path representations are developed for relevant transition probability amplitudes which are valid in the optical frequency regime where the dipole and the rotating-wave approximations apply. Comparisons with numerical results demonstrate the quality of these semiclassical results even in cases in which the wave length of a spontaneously emitted photon becomes comparable or even larger than characteristic length scales of the cavity. This is the dynamical regime in which diffraction effects become important so that geometric optical considerations are typically not applicable.

DOI
10.1051/epjconf/20147804001

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We investigate spontaneous photon emission and absorption processes of two two- level atoms trapped close to the focal points of an ellipsoidal cavity, thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms by describing the field modes semiclassically. Based on this approach, we express the excitation probabilities by a semiclassical photon path representation. Due to the special property of an ellipsoidal cavity of having two focal points, we are able to study interesting intermediate instances between well-known quantum-optical scenarios. Furthermore, the semiclassical photon path representation enables us to address the corresponding retardation effects and causality questions in a straightforward manner.
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We investigate spontaneous photon emission and absorption processes of two two- level atoms trapped close to the focal points of an ellipsoidal cavity, thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms by describing the field modes semiclassically. Based on this approach, we express the excitation probabilities by a semiclassical photon path representation. Due to the special property of an ellipsoidal cavity of having two focal points, we are able to study interesting intermediate instances between well-known quantum-optical scenarios. Furthermore, the semiclassical photon path representation enables us to address the corresponding retardation effects and causality questions in a straightforward manner.
The spectral properties of a photon spontaneously emitted by a material two-level system, modelling an atom or ion, in a parabolic cavity are investigated.In particular, we concentrate on the special case of a motionless two-level system positioned exactly at the focus of a parabolic cavity with a dipole moment oriented along the symmetry axis of this cavity.Treating the corresponding atom-field coupling in the dipoleand rotating wave approximation, it is demonstrated that inside the parabolic cavity the position and frequency dependence of the spectrum of the spontaneously emitted photon exhibits interesting interference patterns.These patterns are explored in detail with the help of a photon path representation of the first-order electric field correlation function.In the radiation, zone the spatial behavior of the spectrum reveals strong interference in particular at distances from the two-level system of the order of the focal length of the parabola.With increasing distances, these interference patterns decay except for an undepleted component surrounding the symmetry axis at an almost constant radius.Furthermore, the maximum of the frequency dependence of the spectrum exhibits a position-dependent frequency shift with respect to the atomic resonance frequency.
Starting from first principles we simulate numerically the dynamics of a system of two-level atoms interacting with a multimode electromagnetic field in a one-dimensional cavity. In particular, we investigate the spontaneous emission of an excited two-level atom in the cavity. We show how the decay depends on the mode spectrum and on the position of the atom in the cavity. We study how the spontaneous emission is modified when the initially excited atom is surrounded by a material medium modeled as a system of two-level atoms. We also study the propagation of photon wave packets emitted by the atom within the material media. Our microscopic model provides us with a deeper understanding of the atom-field interaction and offers us a framework for a systematic investigation of the transition from a microscopic to a macroscopic (phenomenological) description of the spontaneous decay in material media (e.g., dielectrics).