Two-component Bose-Hubbard model with higher-angular-momentum states

Bose-Hubbard Hamiltonian of cold two-component Bose gas of spinor chromium atoms is studied. Dipolar interactions of magnetic moments while tuned resonantly by an ultralow magnetic field can lead to a transfer of atoms from the ground to excited Wannier states with a nonvanishing angular orbital momentum. Hence we propose the way of creating $P_x+i{P}_y$ orbital superfluid. The spin introduces an additional degree of control and leads to a variety of different stable phases of the system. The Mott insulator of atoms in a superposition of the ground and vortex Wannier states as well as a superposition of the Mott insulator with orbital superfluid are predicted.

Figure 1

Phase diagram for 2D square lattice at the resonance $z=4$. The regions are labeled as $M$, Mott insulator with one particle in equal superposition of $a$ and $b$ states; $MS$, superfluid in $a$ and $b$ components ($b$ dominated) and Mott insulator in the orthogonal superposition; $S$, superfluid phase of superposition of $a$ and $b$ components; and $S_b$, superfluid in the $b$ component. In the inset the diagram for $z=3$ together with chemical potential $\mu \left(N\right)$ for a given number of particles obtained from the exact diagonalization. The lines, from bottom to top, correspond to occupation equal to $N=2,...,9$ as indicated. For $\mu >U_b$ (light gray region) the ground state of the system is a two-particle state, therefore in this regime, the phases shown are thermodynamically unstable. They are stable, however, with respect to one particle hopping.

Figure 2

Hopping for the lowest energy state in a $2\times 4$ plaquette obtained from the exact diagonalization. Upper line: $b$ component, lower line: $a$ component.