Dimensional Crossover in the Superfluid-Supersolid Quantum Phase Transition

Supersolids are a fundamental quantum phase of matter where the global phase and translational symmetries are spontaneously broken. The recently discovered supersolidity in quantum gases of strongly magnetic atoms gives the opportunity to explore in depth how superfluidity and crystalline order are mixed in this fascinating phase. The dipolar supersolid is usually created from a Bose-Einstein condensate, i.e., a standard superfluid, crossing a quantum phase transition that is related to the crystallization transitions of ordinary matter. In this work, we assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition. We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first- and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively. The dimensional crossover is peculiar to supersolids, is controlled via the transverse confinement and the atom number, and can be justified on the general ground of the Landau theory of phase transitions. The quasiadiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.