Tunneling dynamics of $^{164}$Dy supersolids and droplets

The tunneling dynamics of a magnetic $^{164}$Dy quantum gas in an elongated or pancake skewed double-well trap is investigated with a time-dependent extended Gross-Pitaevskii approach. Upon lifting the energy offset, different tunneling regimes can be identified. In the elongated trap and for sufficiently large offset, the different configurations exhibit collective macroscopic tunneling. For smaller offset, partial reflection from and transmission through the barrier lead to density accumulation in both wells, and eventually to tunneling-locking. One can also reach the macroscopic self-trapping regime for increasing relative dipolar interaction strength, while tunneling vanishes for large barrier heights. A richer dynamical behavior is observed for the pancake-like trap. For instance, the supersolid maintains its shape, while the superfluid density gets distorted signifying the emergence of peculiar excitation patterns in the macroscopic tunneling regime. The findings reported here may offer new ways to probe distinctive dynamical features in the supersolid and droplet regimes.