Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by the atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength

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.Comment: 10 pages, 5 figure

A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity

We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities