Dicke Model Semiclassical Dynamics in Superradiant Dipolar Phase in the “Bound Luminosity” State

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