Bragg scattering of an ultracold dipolar gas across the phase transition from Bose-Einstein condensate to supersolid in the free-particle regime

We present an experimental and theoretical study of the response of a dipolar supersolid to a Bragg excitation at high-energy defined by the impulse approximation regime. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein condensate to a supersolid state and ultimately to an incoherent array of droplets. Already in the supersolid regime, the observed reduction is faster than the one theoretically predicted by the Bogoliubov-de Gennes theory. By comparing experiments and theories, we are able to attribute this discrepancy to the presence of coherent phase dynamics induced by the crossing of the phase transition. The phase variations are found to change character along the phase diagram and become predominantly incoherent only when reaching the incoherent-droplet regime.