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Journal of Physics A Mathematical and General

Interaction of N atoms with the radiation field in the restricted rotating-wave approximation. II. Numerical results

Miguel Orszag

Published Nov 1, 1979• 4 citations
Publisher

Abstract

For pt.I see ibid., vol.12, no.11, p.2205 (1979). A numerical analysis of the solution of the problem of the interaction of N atoms via the electromagnetic field is presented, using the analytical results of paper I. Several initial conditions are considered for the cases of both spontaneous and stimulated emission. Results show that there is an excellent agreement between the present work and previous numerical results (Walls and Baraka (1970)) in the super-radiant case, while there are differences when the system is initially prepared in the state of complete inversion. These differences are attributed to the restricted rotating-wave approximation, which is the starting assumption in the present work.

DOI
10.1088/0305-4470/12/11/030

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For pt.I see ibid., vol.12, no.11, p.2205 (1979). A numerical analysis of the solution of the problem of the interaction of N atoms via the electromagnetic field is presented, using the analytical results of paper I. Several initial conditions are considered for the cases of both spontaneous and stimulated emission. Results show that there is an excellent agreement between the present work and previous numerical results (Walls and Baraka (1970)) in the super-radiant case, while there are differences when the system is initially prepared in the state of complete inversion. These differences are attributed to the restricted rotating-wave approximation, which is the starting assumption in the present work.
A quantum model of N two-level atoms coupled by a single-mode radiation field under a restricted rotating-wave approximation is studied, assuming a dipole-interaction approximation and that the total number of excitations of the system is conserved. A solution is found for the case of spontaneous emission when the atoms are initially prepared in the state of complete inversion. This solution is valid for all times. A general solution of the model is also found for any initial configuration of the system, in the cases of both spontaneous and stimulated emission. This solution is in a closed form and valid for times tau < tau max .
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.