Unusual behavior of sound velocity of a Bose gas in an optical superlattice at quasi-one-dimension

A Bose gas trapped in a one-dimensional optical superlattice has emerged as a novel superfluid characterized by tunable lattice topologies and tailored band structures. In this work, we focus on the propagation of sound in such a novel system and have found new features on sound velocity, which arises from the interplay between the two lattices with different periodicity and is not present in the case of a condensate in a monochromatic optical lattice. Particularly, this is the first time that the sound velocity is found to first increase and then decrease as the superlattice strength increases even at one dimension. Such unusual behavior can be analytically understood in terms of the competition between the decreasing compressibility and the increasing effective mass due to the increasing superlattice strength. This result suggests a new route to engineer the sound velocity by manipulating the superlattice's parameters. All the calculations based on the mean-field theory are justified by checking the exponent $\gamma$ of the off-diagonal one-body density matrix that is much smaller than 1. Finally, the conditions for possible experimental realization of our scenario are also discussed.