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Non Resonant Case of Energy Exchange Between a Two-Level Atom and a Single Mode Radiation Field

A. Al-Zoudi

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.
In this paper we study the evolution properties along with inversion phenomena of the resonance interactions of a single two-level atom with nnn-mode cavity fields. A general expression of the state for the nnn-mode field is presented. It is found that this atom-field interaction model obeys the Rabi oscillation.
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 N-photon interaction of two two-level atoms with a single-mode quantized radiation field is studied. The general expression for the state vector of the atom–field system is presented with the probability amplitudes in analytic form. For the initial condition in which the atoms are both at their upper levels and the field is in a squeezed state, we study the time evolution of the atomic population inversions and that of the statistics of the field. We find that the ratio of the two coupling constants, the initial squeezing of the field, and N have significant effects on the features of the atoms and of the field.
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.