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Journal of King Abdulaziz University-Science

Atomic Emission Rate Inside a Quantum Resonator

S. Al‐Awfi

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Abstract. We present a general formalism for studying the emission rate of an atom inside a high Q-factor quantum cylindrical resonator. The electromagnetic field structure inside such closed resonator is de-rived. Then the cavity modes are quantised, allowing the position-dependent atomic emission rate to be calculated. Depending on the circumstances, the atomic emission rate may be increased or reduced, and in extreme cases is completely suppressed. Especially, in the quantum size system, the atomic emission rate is possible only via a few cavity modes. The calculations are carried out for the sodium atoms immersed in an empty quantum size resonator. 1.

DOI
10.4197/sci.18-1.6

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Abstract. We present a general formalism for studying the emission rate of an atom inside a high Q-factor quantum cylindrical resonator. The electromagnetic field structure inside such closed resonator is de-rived. Then the cavity modes are quantised, allowing the position-dependent atomic emission rate to be calculated. Depending on the circumstances, the atomic emission rate may be increased or reduced, and in extreme cases is completely suppressed. Especially, in the quantum size system, the atomic emission rate is possible only via a few cavity modes. The calculations are carried out for the sodium atoms immersed in an empty quantum size resonator. 1.
The dipole emission rate inside a hollow resonator with high quality factor Q, which forms a nano quantum dot system is analysed in this paper. The structure modes are firstly quantised, allowing the position-dependent dipole emission rate to be evaluated. In particular, in the nanoscale limit, we show that the dipole emission rate process is can be only produced by a fundamental mode of the system. The effect of the nanoscale limit has been demonstrated to dramatically increase the dipole emission rate. The result is illustrated with reference to sodium atoms placed inside a nano quantum dot resonator with rectangular cross section.
Atomic decay rate process of an excited two-level atom placed inside a cylindrical quantum nanotube is investigated. In particular, when a hole diameter of the cylindrical tube of the order of nanoscale, only the lowest order mode can exist, which means that the system operates as an exact single mode structure. The structure modes are quantised, allowing the position-dependent atomic decay rate process to be evaluated. For an atom inside a cylindrical structure whose typical dimension is in the nanoscale the atomic decay rate process is enhanced compared with that of the same atom in the free space.
We present a quantization procedure for the electromagnetic field in a circular cylindrical cavity. A complete set of vector mode functions satisfying the boundary conditions is obtained utilizing field decomposition. The quantized electromagnetic Hamiltonian is then derived. The conditions for enhancement and inhibition of the spontaneous emission rate per second by an atom inside the cavities are presented in the electric-dipole approximation. Emission is inhibited completely if the cavities are very small. Generally, the behavior is quite complicated; there are many sharp peaks at resonance points and minimal values approach that in free space as the radius of the cavities becomes large.
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.
The conditions for enhancement and inhibition of the spontaneous emission rate per second by an atom inside coaxial cavities are investigated in the electric-dipole approximation. A complete set of vector mode functions satisfying the boundary conditions is obtained utilizing field decomposition, which is needed to quantize the electromagnetic field. The behavior of the emission rate is generally quite complicated; there are sharp peaks at many resonance points, and the minimal values approach unity as the radius of the cavities increases. Emission is usually inhibited completely if the radius is very small. However, under certain conditions, one being a small radius, there is the possibility of very large emission due to the TEM mode.
The normal modes of electromagnetic fields satisfying three different boundary conditions are constructed systematically. For each of these cases, cavity quantization of the electromagnetic fields is carried out explicitly. It is possible, using normal modes, to perform a unitary transformation of the minimal-coupling Hamiltonian of an atom inside the cavity to a multipolar form. It is shown that the boundary condition plays an important role in the transition rates for the spontaneous emission by the atom. Some explicit calculations are carried out for several different boundary conditions. These results become consistent with those for free space in the large-box limit.