Dicke model semiclassical dynamics in superradiant dipolar phase in the 'bound luminosity' state

Analytic solution of semiclassical dynamics equations of the Dicke model in a superradiant state is presented. The time dependences of the amplitudes of superradiant bosonic condensate and coherent two-level atomic array in the microwave cavity prove to be expressed via Jacobi elliptic functions of real time and manifest existence of an adiabatic invariant of motion in the strongly coupled system. The periodic beatings of the photonic and atomic coherent state amplitudes are shifted in time revealing an effect of 'bound luminosity', when energy stored in the two-level system during 'darkness' in the cavity is suddenly converted into photonic condensate that 'illuminates' the cavity for half a period, before it plunges into 'darkness' again