Two-dimensional matter-wave solitons in rotating optical lattices

Abstract

We construct soliton solutions for a self-attractive Bose-Einstein condensate trapped in a rotating optical lattice. The rotation pivot is set at a local maximum of the lattice potential. We demonstrate that fully localized stable solitons, containing $N\ensuremath{\sim}10,000$ atoms, may be supported by the lattice, rotating along with it, if the angular velocity $\ensuremath{\omega}$ is taken below a critical value ${\ensuremath{\omega}}_{c}$ (which is $\ensuremath{\lesssim}10\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$). A monotonously increasing dependence of ${\ensuremath{\omega}}_{c}$ on $N$ is found. In the regime of rapid rotation, the lattice potential is nearly tantamount to the axisymmetric Bessel potential, with a maximum at the center. The latter potential supports fundamental ring-shaped solitons, and also dipole states, which have a bipolar form of two adjacent ring solitons with opposite signs. Stability regions are found for both species (which is the first example of stable azimuthally uniform solitons in a self-focusing model with a radial potential). Unstable solitons of these types evolve into strongly localized nonrotating states. At smaller $\ensuremath{\omega}$, they start to drift slowly, following the rotating lattice. The second critical value, $\ensuremath{\omega}={\ensuremath{\omega}}_{c}^{(2)}$, is found, below which the drifting solitons are destroyed. The rotating lattice supports no stable states in the interval of ${\ensuremath{\omega}}_{c}<\ensuremath{\omega}<{\ensuremath{\omega}}_{c}^{(2)}$.