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Rényi entropy singularities as signatures of topological criticality in coupled photon-fermion systems

F. P. M. Méndez-Córdoba, J. J. Mendoza-Arenas, F. J. Gómez-Ruiz, F. J. Rodríguez, C. Tejedor, and L. Quiroga
Phys. Rev. Research 2, 043264 – Published 20 November 2020

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 Rényi entanglement entropies, between light and matter subsystems. Even though both display singularities at the topological phase transition points, remarkably only the Rényi 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 Rényi 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.

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  • Received 20 July 2020
  • Accepted 13 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043264

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. P. M. Méndez-Córdoba1,*, J. J. Mendoza-Arenas1, F. J. Gómez-Ruiz2,1, F. J. Rodríguez1, C. Tejedor3, and L. Quiroga1

  • 1Departamento de Física, Universidad de Los Andes, A.A. 4976, Bogotá, Colombia
  • 2Donostia International Physics Center, E-20018 San Sebastián, Spain
  • 3Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid 28049, Spain

  • *fp.mendez10@uniandes.edu.co

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Vol. 2, Iss. 4 — November - December 2020

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