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Journal of Mathematical Physics

Exact solution of the Dicke model for the interaction of one atom with the electromagnetic field

Ricardo Ramı́rez, Miguel Orszag

Published Jun 1, 1981• 7 citations
Publisher

Abstract

A formal solution is found for the probability amplitude of emission of a photon by an atom coupled with the electromagnetic radiation, without the assumption of the rotating wave approximation.
DOI
10.1063/1.525024

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International Journal of Optics and Photonics•Jan 15, 2014•0 citations
A quantum theory of second-harmonic generation is presented in which use is made of the formal equivalence that exists between, on the one hand, the emission of a system of N two-level atoms that interact via the electromagnetic field and, on the other, the generation of second harmonics. The N -atom system is described in terms of the Dicke model, but in the so-called ‘restricted rotating-wave approximation’. An analytical, closed-form expression is found for the number of second-harmonic photons as a function of time. Also, a comparison with the semiclassical theory and with experiments is given.
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.