Dicke model semiclassical dynamics in superradiant dipolar phase follows the Euler heavy top

Analytic solution is presented of the nonlinear semiclassical dynamics of superradiant photonic condensate that arises in the Dicke model of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In adiabatic limit with respect to photon degree of freedom the system is approximately integrable and its evolution is expressed via Jacobi elliptic functions of real time. Periodic trajectories of the semiclassical coordinate of photonic condensate either localise around two degenerate minima of the condensate ground state energy or traverse between them over the saddle point. An exact mapping of the semiclassical dynamics of photonic condensate on the motion of unstable Lagrange 'sleeping top' is found. Analytic expression is presented for the frequency dependence of transmission coefficient along a transmission line inductively coupled to the resonant cavity with superradiant condensate. Sharp transmission drops reflect Fourier spectrum of the semiclassical motion of photonic condensate and of 'sleeping top' nodding.