Vortex configurations of bosons in an optical lattice

The single-vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid–Mott-insulator transition, the vortex core has a tendency toward the Mott-insulating phase, with the core particle density approaching the nearest commensurate value. If the nearest-neighbor repulsion exists, the charge-density wave order may develop locally in the core. The evolution of the vortex configuration from the strong- to weak-coupling regions is studied. This phenomenon can be observed in systems of rotating ultracold atoms in optical lattices and Josephson-junction arrays.

Figure 1

(a) The ground-state phase diagram for Bose-Hubbard model at $W=0$ and $\Omega =0$. Lines of equal particle densities are plotted with $⟨N⟩=2.5\text{to}1.5$ from top to bottom. (b) The SF order parameter $⟨a⟩$ vs $⟨N⟩$ at different values of $t∕U=0.1\text{to}0.01$ from top to bottom.

Figure 2

Vortex configurations near the SF-MI phase boundary at $t∕U=0.02$ with bulk particle density $⟨N⟩=1.95$ [in (a) and (b)] and $⟨N⟩=2.05$ [in (c) and (d)]. The left-hand sides [(a) and (c)] are the particle density distributions; the right-hand sides [(b) and (d)] are the SF order distributions.

Figure 3

The evolution of vortex configurations at $⟨N⟩=1.95$ as increasing $t∕U$. SF amplitudes in (a) and particle densities in (b) are shown along a path cut from (10,20) to (30,20) in the $40\times 40$ system. $t∕U=0.02–0.08$ from bottom to top in (a) and top to bottom in (b).

Figure 4

The evolution of vortex particle density distribution at fixed $t∕U=0.03$ (a) and $0.02$ (b) with varying bulk values $⟨N⟩$ along the same path in Fig. 3. (a) From top to bottom, $⟨N⟩=2.3\text{to}1.7$. (b) From top to bottom, $⟨N⟩=1.9\text{to}1.1$.

Figure 5

(a) Phase diagram of the extended Bose-Hubbard model with $W∕U=0.1$ around $⟨N⟩=1.5$. Lines of equal particle densities are plotted with $⟨N⟩=1.6\text{to}1.4$ from top to bottom. The CDW (b) and SF (c) order distributions in the vortex configuration near the CDW phase with $t∕U=0.023$ and bulk average $⟨N⟩=1.5$.