Controlling the character of the superfluid-supersolid quantum phase transition

The recent observation of supersolidity in trapped quantum gases of magnetic atoms has raised much interest about the properties of the so called dipolar supersolid. Besides the combination of superfluidity and crystalline order peculiar to this new state of matter, a fundamental question regards the nature of the quantum phase transition leading to supersolids. In this work we study both experimentally and theoretically the superfluid-supersolid transition, observing that its character changes smoothly between continuous and discontinuous depending on the atom number and transverse confinement. Starting from the Landau theory of phase transitions, we explain this phenomenon as a dimensional crossover between 1D- and 2D-like structures of the supersolid.