Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom

We consider bosons in a Hubbard lattice with an $\text{SU}\left(\mathcal{N}\right)$ pseudospin degree of freedom which is made dynamical via a coherent transfer term. It is shown that, in the basis which diagonalizes the pseudospin coupling, a generic hopping process affects the spin state, similarly to a spin-orbit coupling. This results, for the system in the Mott phase, in a ferromagnetic phase with a variable quantization axis. In extreme cases, it can even give rise to antiferromagnetic order.

Figure 1

Exact diagonalization results for a square lattice with $2\times 2$ sites at $I/U=0.45$. The dashed green line in each plot marks the boundary between Mott and superfluid regime, obtained on the mean-field level as described in Sec. 3a3. (a) Ground-state magnetization with respect to ${\sigma }_z=\frac{N_A-N_B}{N_A+N_B}$. (b) Anticorrelation measured by the magnetic structure factor $S_{\mathbf{q}}$ at $\mathbf{q}=(\pi ,\pi )$. (c) Overlap of the ground state with a product state, given by Eq. (17).

Figure 2

Exact diagonalization results for a square lattice with $4\times 4$ sites and a periodic boundary at $I/U=1/3$. (a) Ground-state magnetization $M$ and anticorrelations measured by the magnetic structure factor $S_{\mathbf{q}}$ at $\mathbf{q}=(\pi ,\pi )$ for $J_{+}=0$ as a function of $J_{-}/U$. (b) Magnetic structure factor $S_{\mathbf{q}}$ at $\mathbf{q}=(\pi ,\pi )$ and overlap of the ground state with a product state, given by Eq. (17), for $J_{-}/U=0.2$ as a function of $J_{+}/U$

Figure 3

Phase boundaries of a 2D system at $J_{+}=0$: the blue line marks the (mean-field) boundary between Mott and superfluid phase. The purple line marks the phase boundary between an ferro- and antiferromagnetically ordered Mott phase. The shaded area marks the region in which an antiferromagnetic Mott phase is expected.

Figure 4

Phase transition on turning the sign of $I$, illustrated for a SU(2) system with three atoms per site.