Supersolid behaviour of a dipolar Bose-Einstein condensate confined in a tube

TL;DR

This paper demonstrates that a dipolar Bose-Einstein condensate confined in a tube exhibits supersolid behavior, characterized by a periodic structure with superfluid properties, as the roton gap closes and the system undergoes a phase transition.

Contribution

The study provides numerical evidence of supersolid formation in a dipolar BEC within a tubular trap, including the effects of quantum fluctuations and excitation spectrum analysis.

Findings

Observation of a roton minimum in the excitation spectrum.

Emergence of a supersolid phase with non-classical inertia.

Transition to a droplet array at lower scattering lengths.

Abstract

Motivated by a recent experiment [L.Chomaz et al., Nature Physics 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a tubular confinement at T=0 within Density Functional Theory, where the beyond-mean-field correction to the ground state energy is included in the Local Density Approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov-de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops in its ground-state a periodic, linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e. (i) a finite non-classical translational inertia along the tube axis and (ii) the appearance, besides the phonon mode, of the Nambu-Goldstone gapless mode corresponding to phase fluctuations, and related to the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.