Probing the topology of the two-photon bands via time-dependent quantum walks

TL;DR

This paper introduces a method to probe two-photon topological invariants in a qubit array using time-dependent quantum walks, advancing the understanding of topological phases in entangled quantum systems.

Contribution

It extends the bulk-boundary correspondence to two-photon states, enabling the measurement of topological invariants in interacting quantum systems.

Findings

Proposes a way to extract two-photon topological invariants from time evolution.

Shows the Zak phase analysis reveals additional topological protection features.

Demonstrates the approach in the interacting Su-Schrieffer-Heeger model.

Abstract

Topological protection of quantum correlations opens new horizons and opportunities in quantum technologies. A variety of topological effects has recently been observed in qubit networks. However, the experimental identification of the topological phase still remains challenging, especially in the entangled many-body case. Here, we propose an approach to independently probe single- and two-photon topological invariants from the time evolution of the two-photon state in a one-dimensional array of qubits. Extending the bulk-boundary correspondence to the two-photon scenario, we show that an appropriate choice of the initial state enables the retrieval of the topological invariant for the different types of the two-photon states in the interacting Su-Schrieffer-Heeger model. Our analysis of the Zak phase reveals additional facets of topological protection in the case of collapse of bound photon pairs.