Crossing the superfluid-supersolid transition of an elongated dipolar condensate

TL;DR

This paper theoretically investigates the dynamical crossing of the superfluid-supersolid transition in an elongated dipolar condensate, analyzing ground states and collective excitations with quantum corrections, and highlights the effects of trap geometry on the transition's nature.

Contribution

It provides a detailed theoretical analysis of the superfluid-supersolid transition in dipolar condensates, including the effects of trap geometry and transition dynamics, extending previous experimental observations.

Findings

Transition can be continuous or discontinuous depending on trap strength.

Axial breathing modes dominate in quasi-1D regimes.

Coupling with transverse modes indicates dimensional crossover.

Abstract

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by G. Biagioni et al. [Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) 1D behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signalling the onset of a dimensional crossover.