  In contrast to the homogeneous superfluid which has only one critical
velocity, there exist two critical velocities for a superfluid in a periodic
potential. The first one, which we call inside critical velocity, is for a
macroscopic impurity to move frictionlessly in the periodic superfluid system;
the second, which is called trawler critical velocity, is the largest velocity
of the lattice relative to the lab frame for the superfluidity to maintain. The
results are relevant to the superfluidity observed in the Bose-Einstein
condensate in an optical lattice and supersolid helium.
