Supersymmetric polarization anomaly in photonic discrete-time quantum walks

TL;DR

This paper demonstrates a topological discrete-time quantum walk using an optical network, revealing a supersymmetric polarization anomaly in midgap states through polarization tomography, advancing understanding of topological effects in quantum systems.

Contribution

It introduces a novel optical implementation of a topological quantum walk that directly observes a supersymmetric polarization anomaly in midgap states.

Findings

Direct observation of polarization anomaly in topological midgap states

Implementation of a single-step protocol combining chiral symmetry and supersymmetry

Full polarization tomography confirming the predicted anomaly

Abstract

Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a system. These anomalies are at the heart of topological effects in fundamental, electronic, photonic and ultracold atomic systems, where they result in a unique response to external fields but generally escape a more direct observation. Here, we implement an optical-network realization of a topological discrete-time quantum walk (DTQW), which we design so that such an anomaly can be observed directly in the unique circular polarization of a topological midgap state. This feature arises in a single-step protocol that combines a chiral symmetry with a previously unexplored unitary version of supersymmetry. Having experimental access to the position and coin state of the walker, we perform a full polarization tomography and provide evidence for the predicted anomaly of the midgap states. This approach opens the prospect to distill topological states dynamically for classical and quantum information applications.