Unveiling the BEC-droplet transition with Rayleigh superradiant scattering

Light scattering plays an essential role in uncovering the properties of quantum states through light-matter interactions. Here, we explore the transition from Bose-Einstein condensate (BEC) to droplets in a dipolar ¹⁶⁶Er gas by employing superradiant light scattering as both a probing and controlling tool. We observe that the efficiency of superradiant scattering exhibits a non-monotonic behavior akin to the rate of sample expansion during the transition, signaling its sensitivity to the initial quantum state, and in turn, revealing the BEC-droplet transition. Through controlled atom depletion via superradiance, we analyze the sample's expansion dynamics and aspect ratio to identify the BEC-droplet phases distinctly, supported by Gaussian variational ansatz calculations. Finally, using these two approaches, we track how the BEC-droplet transition points shift under varying magnetic field orientations. Our work opens new avenues for studying quantum states through superradiance, advancing our understanding of both the BEC-droplet crossover and its coherence properties.