Josephson Oscillations across the BEC-Supersolid Transition in a Dipolar Bose Gas

Since the realization of a supersolid phase in magnetic dipolar Bose gases in 2019, several experiments have explored its superfluidity. In this study, we theoretically investigate a dipolar Bose gas confined in a double-well potential at zero temperature. By comparing the Josephson oscillations in a Bose–Einstein condensate (BEC) and in a supersolid, we examine the characteristics of superfluidity in the supersolid phase. The ground states of the BEC and the supersolid are obtained by numerically solving the extended Gross–Pitaevskii equation (GPE) with the Lee-Huang-Yang quantum correction. Using the phase-imprinting method, we introduced a phase difference into the ground state and analyzed the time-dependent extended GPE with this state as the initial condition. From the results, we clearly identify the characteristic Josephson oscillations in which the population imbalance (difference in particle number between the left and right wells) and the relative phase are mutually coupled and oscillate with the same period. Furthermore, two main findings are obtained: (i) During the transition from the BEC to the superfluid ground state, a pronounced change appears in the amplitude of the Josephson oscillation. (ii) As the system approaches a localized droplet from the supersolid state, the oscillation amplitude decreases and the oscillation period increases.