Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top

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.

Automated summary

Analytic expression for the frequency dependence of transmission coefficient of microwave cavity coupled to transmission line with superradiant condensate is obtained, showing sharp transmission drops that reflect the condensate's frequencies spectrum. These findings pave the way for direct detection of the emergence of superradiant condensates in quantum metamaterials. The results are based on the analytic solutions of the nonlinear semiclassical dynamics of superradiant photonic condensate in the Dicke model, which describes ensemble of dipolar-coupled two-level atoms to electromagnetic field in the microwave cavity. In the ground state, the semiclassical coordinate of the superradiant condensate either oscillates in one of the two degenerate minima of its potential energy or traverses between them over the saddle point, depending on the coupling strength. An experimental setup is proposed for measuring the breakdown of the normal phase of the Dicke model through coupling with the transmission line. Additionally, the semiclassical motion of the superradiant condensate can be mapped to the nodding of an unstable LaGrange sleeping top, making the Dicke model an analog device for modeling mechanical systems dynamics.