Metastability, excitations, fluctuations, and multiple-swallowtail structures of a superfluid in a Bose-Einstein condensate in the presence of a uniformly moving defect

Abstract

We solve the Gross-Pitaevskii (GP) and Bogoliubov equations to investigate the metastability of superfluidity in a Bose-Einstein condensate in the presence of a uniformly moving defect potential in a two-dimensional torus. We calculate the total energy and momentum as functions of the driving velocity of the moving defect and find metastable states with negative effective-mass near the critical velocity. We also find that the first excited energy (energy gap) in the finite-sized torus closes at the critical velocity, that it obeys one-fourth power-law scaling, and that the dynamical fluctuation of the density (amplitude of the order parameter) is strongly enhanced near the critical velocity. We confirm the validity of our results near the critical velocity by calculating the quantum depletion. We find an unconventional swallowtail structure (multiple-swallowtail structure) through calculations of the unstable stationary solutions of the GP equation.