First order structural phase transition between two configurations of a superradiant crystal

We experimentally Synthesize self-organized crystals in an Atomic Bose-Einstein condensate (BEC) of a Rubidium gas by inducing cavity mediated long range interactions. The BEC is placed inside an optical cavity mode and transversely illuminated by a blue detuned pump lattice beam combining a standing wave and a running wave component. Two crystalline phases arise from the couplings to different quadrature of the cavity mode, induced by mode softening in the P-band and S-band of the pump lattice, respectively. The two phases have different non-polar and centrosymmetric structures, connected by a first order phase transition. The transition is thus related to a change of crystal polarization. Thanks to our cavity QED setup, we measure in real-time the transient dynamics of the order parameter across the phase transition by recording the quadrature components of the cavity photon field, where the relaxation frequencies reveal the excitation spectrum of the self-organized crystal.