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 crossover from Bose-Einstein condensate (BEC) to droplets in a dipolar $^{166}$Er 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 crossover. 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 crossover points shift under varying magnetic field orientations. Our results show that superradiance can provide a state-sensitive probe and implement rapid atom-number quenches, opening new avenues for studying quantum states in atomic matter.