Quantum Magnetism with Multicomponent Dipolar Molecules in an Optical Lattice

We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The $1/r^3$ interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with an ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.

Figure 1

The ordering wave vector as the lattice is tilted by angle $\alpha$. As described in the text, for this situation a magnetic field is used to break the degeneracy between ($\mathcal{N}=1,{\mathcal{N}}_z=-1,0,1$) states.

Figure 2

The phase diagram for $V=U$ (left) and $V=0$ (right). For both cases, the dipolar interaction strength was fixed at $\gamma =U/5$. Shown are the antiferromagnetic MI states with one and two bosons per site labeled MI1 and MI2. SF1 and SF2 correspond to superfluid states with partial and complete phase separation (described in text). SF3 is a superfluid phase with no phase separation which has an ordering wave vector that interpolates between the Mott insulating and deep superfluid regime.