The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically, we show, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two-dimensional quantum Hall system. We harness the topological nature of these states to adiabatically pump light across the quasicrystal. We generalize our results to higher-dimensional systems and other topological indices. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.
Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter we directly observe bulk phase transitions, using photonic quasicrystals, by constructing a smooth boundary between topologically distinct one-dimensional quasicrystals. Moreover, we use the same method to experimentally confirm the topological equivalence between the Harper and Fibonacci quasicrystals.
Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping-one of the hallmarks of topological states of matter-was recently realized for photons in a one-dimensional off-diagonal Harper model implemented in a photonic waveguide array. However, if the relationship between topological pumps and quasiperiodic systems is generic, one might wonder how to observe it in the canonical and most studied quasicrystalline system in one dimension-the Fibonacci chain. This chain is expected to facilitate a similar phenomenon, yet its discrete nature hinders the experimental study of such topological effects. Here, we overcome this obstacle by utilizing the topological equivalence of a family of quasiperiodic models which ranges from the Fibonacci chain to the Harper model. Implemented in photonic waveguide arrays, we observe the topological properties of this family, and perform a topological pumping of photons across a Fibonacci chain.
We study the effect of interactions on the propagation of quantum correlations in the bosonic two-body quantum walk. The combined effect of interactions and Hanbury Brown-Twiss interference results in unique spatial correlations which depend on the strength of the interaction, but not on its sign. We experimentally measure the weak interaction limit of these effects using light propagating in a highly nonlinear photonic lattices. Finally, we propose an experimental approach to observe the strong interaction limit using few atoms in optical lattices.
We measure ensemble-averaged quantum correlations of path-entangled photons, propagating in a disordered lattice and undergoing Anderson localization. These result in intriguing patterns, which show that quantum interference leads to unexpected dependencies of the location of one particle on the location of the other. These correlations are shared between localized and nonlocalized components of the two-photon wave function, and, moreover, yield information regarding the nature of the disorder itself. Such effects cannot be reproduced with classical waves, and are undetectable without ensemble averaging.
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