Theory of Steady-State Superradiance

<p>In this thesis, I describe the theoretical development of the superradiant laser, or laser in the\&nbsp;<span style="line-height: 1.6em;">extreme bad-cavity regime. In this regime, the cavity decay rate is much greater than the atomic\&nbsp;</span><span style="line-height: 1.6em;">dynamics. The atoms emit photons into the cavity mode superradiantly in steady state. We\&nbsp;</span><span style="line-height: 1.6em;">develop group-theoretic methods that enable us to exactly solve mesoscopic systems with hundreds\&nbsp;</span><span style="line-height: 1.6em;">of atoms. We demonstrate the synchronization of atomic dipoles in steady-state superradiance.\&nbsp;</span><span style="line-height: 1.6em;">With this synchronized system, we propose conditional Ramsey spectroscopy which allows us to\&nbsp;</span><span style="line-height: 1.6em;">observe Ramsey fringes indefinitely, even in the presence of atomic decoherence. Furthermore,\&nbsp;</span><span style="line-height: 1.6em;">we explore manifestations of synchronization in the quantum realm with two superradiant atomic\&nbsp;</span><span style="line-height: 1.6em;">ensembles. We show that two such ensembles exhibit a dynamical phase transition from two\&nbsp;</span><span style="line-height: 1.6em;">disparate oscillators to quantum phase-locked dynamics. Finally, we study the mechanical effect of\&nbsp;</span><span style="line-height: 1.6em;">the light-atom interaction in the steady-state superradiance. We find efficient many-body cooling\&nbsp;</span><span style="line-height: 1.6em;">of atoms. The work described in this thesis lays the theoretical foundation for the superradiant\&nbsp;</span><span style="line-height: 1.6em;">laser and for a potential future of active optical frequency standards.</span></p>