Hollow cylindrical droplets in a very strongly dipolar condensate

A harmonically trapped Bose-Einstein condensate (BEC) leads to topologically trivial compact states. Because of the long-range nonlocal dipole-dipole interaction, a strongly dipolar BEC revealed many novel phenomena. Here we show that in a strongly dipolar BEC one can have a hollow cylindrical quasi-one-dimensional metastable droplet with ring topology while the system is trapped only in the $x$-$y$ plane by a harmonic potential and a Gaussian hill potential at the center and untrapped along the polarization $z$ axis. In this numerical investigation we use the imaginary-time propagation of a mean-field model where we include the Lee-Huang-Yang interaction, suitably modified for dipolar systems. Being metastable, these droplets are weakly stable and we use real-time propagation to investigate its dynamics and establish stability.