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

Abstract

A broad range of phenomena in correlated electrons traveling in moir\'e 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 $^{23}\mathrm{Na}$ atoms lying in a single layer having a moir\'e 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 moir\'e lattice defined by a specific angle $\ensuremath{\theta}$ plus a harmonic confinement. To demonstrate the persistence of such an initial condition under the competence of the moir\'e 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 moir\'e lattices we found a dynamic stability for angles larger than a special one ${\ensuremath{\theta}}_{s}$, 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 moir\'e lattices exhibit the dynamic stability starting from a certain angle that also depends on the harmonic confinement for the noninteracting case.