Figure 1

Quantum phase diagram for Anderson localization of pairs in a 1D quasiperiodic lattice. The critical potential strength is plotted as a function of the interaction (energy units $J=1$). The dashed line corresponds to the asymptotic regime of tightly bound pairs where AL occurs at ${\Delta }_{\mathrm{cr}}=-2/U$. The phase diagram applies to both attractively and repulsively bound pairs.Reuse & Permissions

Figure 2

Crossing the phase boundary of Fig. 1. Local density $n_i$ (left panel) and quasimomentum distribution $n_k$ [normalized to $\int n_{k}dk/(2\pi )=2$] (right panel) of atoms inside molecules for fixed value of $U=-3$ and increasing values of the potential strength (starting from the top). At $\Delta ={\Delta }_{\mathrm{cr}}=0.544$ the molecular state becomes Anderson localized. We used $\theta =\pi /5$ and $L=233$ [30].Reuse & Permissions

Figure 3

Main panel: Binding energy of molecules versus interaction for increasing values of the potential strength $\Delta =1$ (bottom), 1.5, 2, 2.5. The asymptotic behaviors for strong and weak interactions, obtained from Eq. (6, 7), respectively, are shown with dashed lines. Diamonds correspond to the predictions of the variational ansatz (12). Upper left panel: $A\sigma$ [cf. Eq. (8)] and ${\alpha }_1$ [cf. Eq. (9)], as a function of the potential strength. Also shown is the asymptotic behavior of ${\alpha }_1$ for $\Delta \gg 1$. Right panel: best variational parameter $\eta$ as a function of the interaction strength $|U|$ and for the same values of $\Delta$ as in the main panel ($\Delta =2$ is the top curve near $U=0$).Reuse & Permissions