Title: Rotational Superradiance in a Time-Reversal Symmetry-Broken Quantum Gas inside an Optical Cavity

Abstract: Appearance of quantized vortices in a superfluid and a Bose-Einstein condensate (BEC) stems from their nontrivial response to broken time-reversal symmetry (TRS). Here we show that breaking of the TRS by, for example, rotation or an external synthetic magnetic field in a transversely-driven BEC coupled to a single mode of an optical cavity modifies drastically Dicke-superradiance and self-ordering phenomena in this system. In particular, photon scattering from the pump laser into the cavity is amplified by the rotational motion of the BEC, leading to so-called 'rotational superradiance' - in a loose analogy to black-hole physics - with distinct critical scaling properties. Another notable finding is that cavity photons mediate long-range, periodic attractive interactions among the vortices, which compete with pair-wise logarithmic repulsive vortex interactions and deform the Abrikosov triangular vortex lattice favoring a stripe-like pattern. Remarkably, the rotation of the BEC and topological properties of the vortex lattice can be monitored nondestructively through the cavity output field.