R\'enyi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems

TL;DR

This paper demonstrates that topological phase transitions in a photon-fermion system can be detected through measurable cavity observables linked to Rényi entropy singularities, enabling experimental access to quantum entanglement features.

Contribution

It establishes a direct connection between Rényi entropy singularities and experimentally accessible photon observables in topological systems.

Findings

Rényi entropy exhibits singularities at topological transition points.

Fano factor correlates with Rényi entropy and signals phase transitions.

Method proposed for measuring bipartite entanglement via cavity observables.

Abstract

We show that the topological phase transition for a Kitaev chain embedded in a cavity can be identified by measuring experimentally accessible photon observables such as the Fano factor and the cavity quadrature amplitudes. Moreover, based on density matrix renormalization group numerical calculations, endorsed by an analytical Gaussian approximation for the cavity state, we propose a direct link between those observables and quantum entropy singularities. We study two bipartite entanglement measures, the von Neumann and R\'enyi entanglement entropies, between light and matter subsystems. Even though both display singularities at the topological phase transition points, remarkably only the R\'enyi entropy can be analytically connected to the measurable Fano factor. Consequently, we show a method to recover the bipartite entanglement of the system from a cavity observable. Thus, we put forward a path to experimentally access the control and detection of a topological quantum phase transition via the R\'enyi entropy, which can be measured by standard low noise linear amplification techniques in superconducting circuits. In this way, the main quantum information features of Majorana polaritons in photon-fermion systems can be addressed in feasible experimental setups.