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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Dicke superradiance from atomic systems with dipolar coupling

F. De Martini

Published Jun 1, 1974• 1 citation
Publisher
DOI
10.1007/bf02819377

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Here we present an approach to the problem of superradiance in dense atomic samples, when dipolar interactions arise between atoms. Our treatment consists of the sequential use of the Holstein-Primakoff and mean-field approximations, from which we derive master equations for the strong and weak couplings of the sample with the reservoir. We find, in both cases, that the radiation emission presents remarkable features, with characteristic emission times much shorter and intensities much higher than those of Dicke superradiance. In particular, for strong sample-reservoir coupling, a whole comb of superpulses occurs within an envelope with the above-mentioned characteristic emission times much shorter and intensities much higher than those of Dicke superradiance.
Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange ``sleeping top'' also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.