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Physical Review A

Spontaneous emission from an atom in a nonideal cavity: Application of a generalized master equation

R.W.F. van der Plank, L.G. Suttorp

Published Sep 1, 1996• 3 citations
Publisher

Abstract

The decay of an excited two-level atom in a cavity with mirrors of finite transmittivity is studied with the help of a generalized multimode master equation that has been established recently. The time evolution of the decaying atom is obtained by accounting for the interaction with infinitely many quasimodes. The analytical and numerical results are compared with those of the standard multimode master equation and of a universe-mode approach. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2464

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The decay of an excited two-level atom in a cavity with mirrors of finite transmittivity is studied with the help of a generalized multimode master equation that has been established recently. The time evolution of the decaying atom is obtained by accounting for the interaction with infinitely many quasimodes. The analytical and numerical results are compared with those of the standard multimode master equation and of a universe-mode approach. \textcopyright{} 1996 The American Physical Society.
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We present a numerical and analytical study of a multimode Jaynes-Cummings model describing the spontaneous decay of a single atom in a high-Q cavity. The theory of cavity-modified spontaneous emission is discussed in terms of quantities that have clear physical interpretations: the photon wave packet radiated by the atom, its reflection by the cavity boundaries, and its reabsorption by the atom. Multimode corrections to the single-mode Jaynes-Cummings model are calculated. The multimode corrections are formulated in terms of quantities that may be calculated by solving the single-mode equations of motion.
Spontaneous emission from a system of NNN identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state ∣z0〉|{z}_{0}〉∣z0​〉.
Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed position in a nonideal cavity. For this case we find a modification of the damped Rabi oscillations, which depends on the atomic position. \textcopyright{} 1996 The American Physical Society.