Superradiant phases of an atomic beam traversing an optical cavity

We investigate the different emission regimes of a pre-excited and collimated atomic beam passing through a single mode of an optical cavity. In the regime where the cavity degrees of freedom can be adiabatically eliminated, we find that the atoms undergo superradiant emission when the collective linewidth exceeds transit-time, homogeneous, and inhomogeneous broadening mechanisms. After the first superradiant emission we find that the system can reach a plethora of different dynamical superradiant phases depending on the detuning of the atomic transition and the cavity mode, the Doppler-width of the atomic beam, and the angle between the cavity and the atomic beam axis. Our findings highlight the ability of driven-dissipative many-body systems to form coherent dynamical structures that are stable on timescales that exceed the lifetime of all their constituents.