Cold atoms in a rotating optical lattice with nearest-neighbor interactions

Extended Bose-Hubbard models with nearest-neighbor interaction describe minimally the effect of long-range interaction on ultracold atoms in deep optical lattices. The rotation of such optical lattices subjects such neutral cold atoms to the effect of an artificial magnetic field. The modification of the phase boundaries of the density-wave and Mott-insulator phases due to this rotation are shown to be related to the edge spectrum of spinorial and scalar Harper equations. Corresponding profiles of the checkerboard vortex states with sublattice modulated superfluid order parameter near the density-wave phase boundary are calculated.

Figure 1

(a) Alternating particle number in density-wave phase and (b) superfluid order parameter in supersolid phase on the sites of A [(red) dark gray] and B [(green) light gray] sublattices.

Figure 2

(a) Hofstadter butterfly: the dimensionless energy ($\varepsilon$) spectrum for Eq. (8) for various $\nu \{0,1\}$. The upper edge [marked (red) dark gray] gives the boundary of the density wave and the Mott-insulator lobe as explained in the text. (b) The first DW and MI lobe as a function of $t,\mu ,\nu$ in mean-field approximation where $t$ and $\mu$ are in units of $U$ and are dimensionless. (c) Cross section of the plots in (b) that shows the modification of the first two density-wave lobes and the first Mott-insulator lobe at various values of circulation quanta $\nu$. In all these plots, $V$ has been taken as $0.2$ in units of $U$.

Figure 3

(a) Checkerboard vortices at the density-wave ($|2,1,2,1,\dots \rangle$) phase boundary ($\mathrm{t̃}={\mathrm{t̃}}_c$) corresponding to the highest eigenvalue (the edge) of the Hofstadter butterfly spectrum for $\nu =\frac{1}{16\times 16}$. The direction of the arrow gives ${\phi }_{i_A,i_B}$, while the color axis gives the superfluid density. The superfluid density is normalized by the maximum superfluid density (and hence is dimensionless) at the boundary. The $x$ and $y$ coordinates are given in units of optical lattice spacing and are the same in all the plots. (b) Corresponding DW order parameter (along the $z$ axis). (c) More complicated vortex structure corresponding to the higher value of $\mathrm{t̃}$ corresponding to a lower eigenvalue $[254(16\times 16-2)$th band] and (d) corresponding DW order parameter.