Topology in Photonic Discrete-Time Quantum Walks: A Comprehensive Review

Abstract

We present a comprehensive review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains. Moreover, we introduce a novel scheme for DTQWs using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects in photonic systems.

Topological weak-measurement-induced geometric phases revisited

“…Geometric phases can be held responsible for a number of situations: they can modify material properties in solids, such as conductivity in graphene [4], they can trigger the emergence of surface edge-states in topological insulators, whose surface electrons experience a geometric phase [5], they can modify the outcome of molecular chemical reactions [6], and they can affect electronic properties of matter [7]. Furthermore, understanding various physical phenomena [8][9][10], defining fractional statistics anyonic quasiparticles [11][12][13], and identifying topological invariants for quantum Hall phases [14], superconductors [15,16], or quantitative characterizations of topological insulators via the Zak phase [17,18], as well as underpinning holonomic and topological signatures in photonic systems [19][20][21][22][23], are all made possible by geometric phases.…”