Enhancing quantum coherence with short-range correlated disorder

We introduce a two-dimensional short-range correlated disorder that is the natural generalization of the well-known one-dimensional dual random dimer model [D. H. Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)]. We demonstrate that, as in one dimension, this model induces a localization-delocalization transition in the single-particle spectrum. Moreover we show that the effect of such a disorder on a weakly interacting boson gas is to enhance the condensate spatial homogeneity and delocalization and to increase the condensate fraction around an effective resonance of the two-dimensional dual dimers. This study proves that short-range correlations of a disordered potential can enhance the quantum coherence of a weakly interacting many-body system.

Figure 1

Schematic representation of (a) the unperturbed Hamiltonian, (b) the Hamiltonian in the presence of a single impurity, (c) the effective Hamiltonian after decimation of site 0 in the Hamiltonian (a), and (d) the effective Hamiltonian after decimation of site 0 in the Hamiltonian (b).

Figure 2

Schematic representation of the 2D DRDM.

Figure 3

Inverse participation ratio $[ln(\mathcal{I})$ in the left column and $ln\left(\mathcal{I}{L}^2\right)$ in the right column] as a function of the energy $E$ in units of $t$. The plots in the first row correspond to $\mathrm{\Delta }/t=0.44$ and $t^{\prime }/t=1.2$; those in the second row correspond to $\mathrm{\Delta }/t=3$ and $t^{\prime }/t=2$, and those in the the third row correspond to $\mathrm{\Delta }/t=8$ and $t^{\prime }/t=3$. The different curves in each plot correspond to different system sizes: $L=20$ (red pluses), 30 (green crosses), 40 (blue asterisks), and 50 (magenta squares). Each curve correspond to $N_{\mathrm{imp}}/N\simeq 0.15$ and to an average over 50 configurations. The data are binned in 80 (first row) and 110 (second and third rows) bins. The vertical dashed lines indicate $E_{\mathrm{res}}$.

Figure 4

The exponent of Eq. (7) as a function of the energy for $\mathrm{\Delta }/t=8$ and $t^{\prime }/t=3$. The exponent has been obtained using calculations for lattice-linear dimensions $L=40,50,60,70,80,90,100$ averaged over 20 realizations; the error bars correspond to the standard deviation of the fit of the data to Eq. (7). The vertical dashed line indicates $E_{\mathrm{res}}$.

Figure 5

${\mathcal{I}}_{\mathrm{GS}}{L}^2$ as a function of $\mathrm{\Delta }/t$ for $L=20, U/t={10}^{-2}$, and $n=20$ particles per site. The different curves correspond to different values of $t^{\prime }$ as indicated in the legend. The solid symbols correspond to the 2D-DRDM potential, and the open symbols correspond to the UN-RAND potential.

Figure 6

${\mathcal{I}}_{\mathrm{GS}}{L}^2$ as a function of $\mathrm{\Delta }/t$ for $L=20, U={10}^{-2}t$, and $t^{\prime }/t=2$. The different curves correspond to different values of the average density $n$ as indicated in the legend. All the curves correspond to the 2D-DRDM potential. The vertical dashed line indicates the noninteracting resonance condition given in Eq. (11).

Figure 7

Boxes of different sizes, in the presence and in the absence of an impurity.

Figure 8

${\mathcal{I}}_{\mathrm{GS}}{L}^2$ as a function of $\mathrm{\Delta }/t$ for $t^{\prime }/t=2, U/t={10}^{-2}$, and $n=20$ particles per site. The different curves correspond to different values of $L$ as indicated in the legend. The solid symbols correspond to the 2D-DRDM potential, and the open symbols correspond to the UN-RAND potential.

Figure 9

Lattice density plots together with site and bond impurities locations for $t^{\prime }/t=2, \mathrm{\Delta }/t\simeq 2$ and (top)DRDM disorder and (bottom) UN-RAND.

Figure 10

Same as Fig. 9 for $\mathrm{\Delta }/t=6.6$.

Figure 11

Same as Fig. 9 for $\mathrm{\Delta }/t=15.1$.

Figure 12

Condensate fraction $n_c$ as a function of $\mathrm{\Delta }/t$ for $t^{\prime }/t=2, U/t={10}^{-2}$, and $n=20$ particles per site. The different curves correspond to different values of $L$ as indicated in the legend. The solid symbols correspond to the 2D-DRDM potential, and the open symbols correspond to the UN-RAND potential.