Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks

Abstract

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete-step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time-dependence or micromotion in discrete-step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete-step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics.

12 pages main text plus 7 pages of apppendix (19 pages total). Published version

References in corpus (11)

• Topological characterization of periodically-driven quantum systems
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Realization of an anomalous Floquet topological system with ultracold atoms
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Tuning anomalous Floquet topological bands with ultracold atoms
• Topological properties of Floquet winding bands in a photonic lattice
• Superfluidity of Light and its Break-Down in Optical Mesh Lattices
• Estimating bulk and edge topological indices in finite open chiral chains
• Topological Quantum Walk with Discrete Time-Glide Symmetry
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Relative homotopy approach to topological phases in quantum walks

Cited by in corpus (3)

• A comprehensive review on developments of synthetic dimensions
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• Anomalous Floquet Phases. A resonance phenomena