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arXiv:1909.12492 · Journal of Physics B Atomic Molecular and Optical Physics

Radiation properties of an oscillating atom in the presence of external fields

F Chegini, F Kheirandish, M R Setare

Published Nov 19, 2019• 0 citations
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Abstract

Abstract In the first part of the present work, the correction to the photon emission rate of an oscillating two-level atom in the presence of an electromagnetic quantum vacuum field has been investigated for two different configurations: (i) an atom is trapped in the vicinity of a perfect conductor and (ii) an atom is trapped between two perfect conductors. In the second part, the correction to the decay rate of an initially excited oscillating two-level atom due to the presence of a perfectly conducting surface is found.

DOI
10.1088/1361-6455/ab5905

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Abstract In the first part of the present work, the correction to the photon emission rate of an oscillating two-level atom in the presence of an electromagnetic quantum vacuum field has been investigated for two different configurations: (i) an atom is trapped in the vicinity of a perfect conductor and (ii) an atom is trapped between two perfect conductors. In the second part, the correction to the decay rate of an initially excited oscillating two-level atom due to the presence of a perfectly conducting surface is found.
The interaction between electromagnetic radiation and two two-level atoms with different resonance frequencies near a perfectly conducting metal surface is considered. The atom-atom and atom-surface separations are assumed to be smaller than the corresponding mean resonance wavelength. A quantum-mechanical version of the image method is adopted to study the spontaneous emission by such an atomic pair. Within the framework of this approach, each individual atom and its corresponding image are kinematically correlated, while dynamically they are in effect independent. The total radiation rate of the atomic system is calculated as a function of time for various values of frequency difference. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some initially act as photon-trapping states and eventually are able to undergo radiative decay. Oscillations as a manifestation of beating appear in the time evolution of the radiation rate in all cases of the various initial states, when the frequency difference becomes larger than a critical value given as twice the mean halfwidth of the atomic resonance lines.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
It is a well known fact that the presence of material bodies in the vicinity of an atom affects its interaction with the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous-emission rate of a given excited atom is altered when this atom is placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism upon which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom, but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. The oscillatory pattern for the spontaneous-emission rate of the atom as we vary its relative position to the wedge as well as the phenomenon of suppression are shown by a few graphs.
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.
Abstract One of the greatest successes in quantum theory, and certainly one of the more important parts for application to devices and applications is the prediction of the emission of light through the quantization of an electromagnetic field. Broadly, this is the field of quantum electrodynamics. In this chapter, we develop the Hamiltonian for the classical electromagnetic field. It is seen that the Hamiltonian for each mode (identified by the k-vector and polarization of the field) of the plane wave electromagnetic field is identical to that of the harmonic oscillator. One unit of energy, ℏω, in a mode is a called a photon. The eigenkets for the system are number states (Fock states). We then consider a two-level system described by a Hamiltonian which couples the two-level quantum system to the quantized electromagnetic field. Using the Weisskopf–Wigner formalism developed in Chapter 14, we solve the equations of motion for the time dependent Schrödinger equation assuming the system starts in the excited state with no radiation present in the vacuum field. The results show the creation of one unit of energy in an electromagnetic mode corresponding to the emission of a photon. The excited state probability decays exponentially with the emission of this photon. We consider the important and special case of such a two-level system but in a cavity restricting the radiation field to a single mode. The Jaynes–Cummings Hamiltonian shows that this system, if started in the excited state, Rabi oscillates with no radiation incident on the system.
We consider the situation where a two-level atom is placed in the vicinity of the center of a spherical cavity with a large numerical aperture. The vacuum field at the center of the cavity is actually equivalent to the one obtained in a microcavity, and both the dissipative and the reactive parts of the atom's spontaneous emission are significantly modified. Using an explicit calculation of the spatial dependence of the radiative relaxation rate and of the associated level shift, we show that for a weakly excitating light field, the atom can be attracted to the center of the cavity by vacuum-induced light shifts.