Aharonov-Bohm Caging and Inverse Anderson Transition in Ultracold Atoms

Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.

Figure 1

The experimental scheme and energy spectrum of the Aharonov-Bohm cage. (a) Schematic diagram of a rhombic lattice with three sites ($A_n$, $B_n$, and $C_n$) per unit cell. The sites $A_n(n=0,1,\dots )$ are put on the $F=2$ energy level, while the $B_n$ and $C_n(n=0,1,\dots )$ sites are rooted in the $F=1$ energy level. The complex hopping coefficients between nearest-neighboring sites are denoted as $J{e}^{i{\theta }_m}$ ($m=1$, 2, 3, 4). In our experiment, we choose the gauge by setting ${\theta }_1=\varphi$ and $\mathrm{others}=0$. (b) The energy dispersion $E(k)$ of the chain as a function of the flux $\varphi$ (middle). The left and right insets display the dispersion relation for $\varphi =\pi$ and $\varphi =0$, respectively.

Figure 2

Aharonov-Bohm cage dynamics. (a) The Aharonov-Bohm cage evolution with flux $\varphi =\pi$ in each plaquette. (b) Measuring the population distribution of sites $A$, $B$, and $C$ in 1 ms. The AB cage effect appears in the middle adjacent unit cells. The small population leakage of the middle cage can be mainly ascribed to the imperfect experimental parameters. The solid lines represent the fitting of experimental data [57]. (c) The evolution dynamics with flux $\varphi =0$ in each plaquette. (d) The population distribution of sites $A$, $B$, and $C$ in the middle unit cell with flux $\varphi =0$. All the fitted solid lines show a fast exponential decay feature [57]. In (a) and (c), the population of all lattice sites has been normalized in each displayed time instant. In (b) and (d), the blue dots and lines represent the total population in the caging unit including sites $A_0,B_0,B_{-1},B_0,B_0$.

Figure 3

The localization and transport with symmetric vs antisymmetric correlated disorder. (a) Schematic diagram of adding on-site disorders. (b) The momentum lattices evolution of ballistic transport with the antisymmetric on-site disorder. (c) The momentum lattices evolution of AB cage localization with the symmetric on-site disorder. (d) The compared evolutions of distance $\mathcal{D}(t)$ with a different type of on-site disorder [58]. All above results are set with flux $\varphi =\pi$. In (b) and (c), the population has also been normalized in each displayed moment. The above experimental results refer to a single realization of correlated Bernoulli disorder.

Figure 4

The energy bands and evolution with antisymmetric Bernoulli disorder. (a) The quasienergy spectrum for different on-site disorder strengths, where we have calculated eigenvalues of a chain with 100 unit cells. The left and right inset correspond to the smallest and largest bandwidth, respectively. (b) The measured distance with various disorder strengths in 0.6 ms. The inset line corresponds to the theoretical calculated distance. The above measurements refer to a single realization of Bernoulli disorder.