Dynamic stability in spinor Bose gases in moir? lattices with square and hexagonal symmetries

A broad range of phenomena in correlated electrons traveling in moire lattices has emerged in both scenarios, experiments and theory. In this paper we report the observation of a dynamic stability that arises in an analogous system to that of electrons, a weakly interacting spinor Bose gas of ultracold 23Na atoms lying in a single layer having a moire pattern with square and hexagonal symmetries. Our paper is based on the dynamical description of two magnetic domains represented by two hyperfine spin components of a Bose condensate initially localized in the left and right halves of a moire lattice defined by a specific angle 0 plus a harmonic confinement. To demonstrate the persistence of such an initial condition under the competence of the moire pattern and harmonic confinements we studied both single noninteracting and double-domain interacting cases. We solve the time dependent Gross-Pitaevskii equations, and track the time evolution of several observables on each half as a function of the twisting angle. In the case of square moire lattices we found a dynamic stability for angles larger than a special one 0s, except for the Pythagorean angles. The value of such an angle depends on the existence of a harmonic trap when interactions are absent, while this dependence is negligible for the interacting case. Hexagonal moire lattices exhibit the dynamic stability starting from a certain angle that also depends on the harmonic confinement for the noninteracting case.