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Analytic expression is found for the frequency dependence of transmissioncoefficient of a transmission line inductively coupled to the microwave cavitywith superradiant condensate. Sharp transmission drops reflect condensate'sfrequencies spectrum. These results pave way to direct detection of emergenceof the superradiant condensates in quantum metamaterials. Results are based onthe analytic solutions of the nonlinear semiclassical dynamics of superradiantphotonic condensate in the Dicke model of an ensemble of two-level atomsdipolar coupled to the electromagnetic field in the microwave cavity. Inadiabatic limit with respect to photon degree of freedom the system isapproximately integrable, with evolution being expressed via Jacobi ellipticfunctions of real time. Depending on the coupling strength, the semiclassicalcoordinate of superradiant condensate in the ground state either oscillates inone of the two degenerate minima of condensate's potential energy or traversesbetween them over the saddle point. An experimental setup for measuring of thebreakdown of the normal phase of the Dicke model via coupling to thetransmission line is proposed. A one-to-one mapping of semiclassical motion ofsuperradiant condensate on the nodding of unstable Lagrange "sleeping top" alsoturns Dicke model into analogue device for modelling dynamics of mechanicalsystems.

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