Magnetic phases of two-component ultracold bosons in an optical lattice

We investigate spin-order of ultracold bosons in an optical lattice by means of dynamical mean-field theory. A rich phase diagram with anisotropic magnetic order is found, both for the ground state and at finite temperatures. Within the Mott insulator, a ferromagnetic to antiferromagnetic transition can be tuned using a spin-dependent optical lattice. In addition we find a supersolid phase, in which superfluidity coexists with antiferromagnetic spin order. We present detailed phase diagrams at finite temperature for the experimentally realized heteronuclear ${}^{87}\text{R}\text{b-}{}^{41}\text{K}$ mixture in a three-dimensional optical lattice.

Figure 1

(Color online) Illustration of the cavity method. Sites which are connected to the impurity (colored greenish) have one neighbor less once the impurity is removed.

Figure 2

(Color online) Single component phase diagram for various temperatures as obtained by BDMFT. In the inset: number fluctuations for density $n=1$ and $T=0$. The lattice coordination number is chosen as $z=6$.

Figure 3

(Color online) Phase diagram of a two-component bosonic mixture (in an optical lattice with $z=4$) at total density $n_1+n_2=1$ for different temperatures and ratios of the interspecies to the intraspecies interaction.

Figure 4

(Color online) Phase diagram of a ${}^{87}\text{R}\text{b-}{}^{41}\text{K}$ mixture (for $z=6$) at fixed total density $n_{\text{Rb}}+n_{\text{K}}=1$ as a function of lattice depth $s$ and Rb-K scattering length in units of the Bohr radius.