Fermion parity switches imprinted in the photonic field of cavity embedded Kitaev chains

TL;DR

This paper investigates how fermion parity switches in a finite Kitaev chain influence the photonic field within a cavity, revealing potential experimental signatures of topological phases through photon measurements.

Contribution

It demonstrates that photon number and quadratures peak at parity switching points, linking topological features to observable photonic properties, and compares exact and mean field methods for analysis.

Findings

Photon number peaks at parity switching points.

Photonic quadratures reveal squeezed states.

Mean field approach fails for odd photonic states.

Abstract

We study a finite-length Kitaev chain coupled to a single mode photonic cavity. The topological phase of the finite-length Kitaev chain is characterized by the presence of fermion parity switching points that correspond to the degeneracy between even and odd parity ground states. Using exact diagonalization, we compute the many-body energy spectrum of the electron-photon Hamiltonian and we find that the ground state in the topological phase of the Kitaev chain is only weakly affected by the cavity coupling. This is in contrast with the excited states showing strong dependence on the cavity frequency. We find that the photon number and the photonic field quadratures peak at values of the chemical potential corresponding to parity switching points revealing a property of the finite-length Kitaev chain in the topological phase. This later finding suggests that quantum optics experiments could be used to detect topological features of the Kitaev chain embedded into a photonic cavity. Moreover, calculations of photonic quadratures reveal squeezed states that are both captured by the exact diagonalization technique and mean field decoupling. However, the mean field approach fails to correctly capture the photonic probability in the odd photonic states.