Mean-field phase diagram of cold lattice bosons in disordered potentials

We address the phase diagram of the disordered Bose-Hubbard model that has been realized in several recent experiments in terms of optically trapped ultracold bosons. We show that a systematic description of all of the expected quantum phases can be obtained at both zero and finite temperature via a site-dependent decoupling mean-field approach. Also, we relate the boundaries of the Mott-insulating phase to an off-diagonal noninteracting Anderson model whose spectral features provide an avenue for determining the debated nature of the phase surrounding the Mott lobes. Our approach is simple yet effective, and scalable to systems with experimentally relevant sizes and features.

Figure 1

(Color online) Phase diagrams for a 100-site disordered lattice for two values of the strength $\Delta$ of the random potential.

Figure 2

(Color online) Spectral density $\sigma \left(ϵ\right)$ of $Q$ vs $\mu$ for a lattice comprising $M={10}^6$ sites and the same $\Delta$’s as in Fig. 1. The spectra are normalized so that $q_M$ corresponds to $ϵ=1$.

Figure 3

(Color online) Square modulus (left) and phase differences (right) of ${\alpha }_m^{\left(\theta \right)}$ along the dashed line in the right panel of Fig. 1 ($\Delta =0.25$, $\mu =0.35$, $\theta ={10}^{-3}$).

Figure 4

The same phase diagrams as in Fig. 1 at a finite temperature $T=0.01U∕k_B$. Filled and empty circles in the legend denote finite and zero values for the relevant quantity.