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Physical Review A

Energetics of radiation and a two-level atom in an ideal resonant cavity

G. J. Papadopoulos

Published Apr 1, 1988• 14 citations
Publisher

Abstract

The problem of a two-level atom and M degenerate modes of radiation interacting with the atom is solved exactly within the rotating-wave approximation. The results are applied for obtaining the evolution of energy distribution in the atom and the various modes resonant to the atom in an ideal cavity. For a small number of modes the atomic oscillation and the total radiant energy exhibit irregularities in their evolution patterns, while considerable amounts of energy are being transferred from one mode to the other. As the number of modes increases, regular patterns emerge in the atomic oscillation and the total radiation, while only small movements of energy appear among the modes.

DOI
10.1103/physreva.37.2482

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The problem of a two-level atom and M degenerate modes of radiation interacting with the atom is solved exactly within the rotating-wave approximation. The results are applied for obtaining the evolution of energy distribution in the atom and the various modes resonant to the atom in an ideal cavity. For a small number of modes the atomic oscillation and the total radiant energy exhibit irregularities in their evolution patterns, while considerable amounts of energy are being transferred from one mode to the other. As the number of modes increases, regular patterns emerge in the atomic oscillation and the total radiation, while only small movements of energy appear among the modes.
The quantum mechanical analysis for a non-resonant case of a single radiation mode interacting with a two-level atom in a cavity is studied. Expressions for the mean value of photon number and the time evolution of the atomic motion are given. The frequency of exchange energy between the atomic levels and the radiation field systems for non- resonant and resonant interactions is obtained. Results for all initial states of the atom-radiation field are presented. Results for resonant and non-resonant interactions are compared.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
We study the dynamics of a system consisting of a two-level atom and a quantum oscillator coupled by the vacuum radiation field. The oscillator and the atom are assumed to have the same resonance frequency. In contrast to the two-atom or two-oscillator case, the atom-oscillator system leads to an unclosed hierarchy of equations for the operators that determine the radiation pattern emitted by the atom-oscillator system. Instead of using the operator equations, we formulate the problem in terms of density-matrix equations which can be solved once the initial conditions are specified. As an example, we looked at the radiation pattern, the decay dynamics, and the spectrum for an initial condition in which the oscillator is in its n=1n=1n=1 state and the atom is in its excited state. Dressed states (dressed by the static interaction between the atom and oscillator) prove to be especially useful for interpreting the results and comparing them with the two-atom and two-oscillator systems. All calculations are carried out using the resonance or rotating-wave approximation. The relationship of our work to damped Jaynes-Cummings models is noted.
In this paper the dynamics of wave fields in a cavity with one sinusoidally moving mirror are investigated. The wave equation is solved approximately using the method of multiple time scales. Frequency shifts as well as amplitude and phase modulations of cavity modes are given. In all cases when it is possible, an approximate effective field Hamiltonian operator is derived. In the adiabatic case it is then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic motion of a mirror can lead to suppression of the Rabi oscillations of atomic inversion.
A method utilising the coherent state variables for the electromagnetic field and appropriate spin variables for two-level atomsis developed for obtaining the dynamical evolution of the field and the atoms separately. The case of a single radiation mode interacting with two two-level atoms is studied. The time evolution of the photon number, starting from n photons and both atoms at their higher levels, is given. Furthermore, when the initial state consists of n photons and one of the atoms in its excited state with the other in its ground state, the temporal development of the photon number, as well as the motion of each atom, are obtained. In the latter case it becomes apparent that energy exchange takes place among the atomic systems, while the field acts as a transfer agent.