Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schr\"odinger Cat States

TL;DR

This paper explores how coupling a topological Kitaev chain to a cavity enables control over Majorana zero modes, revealing non-Abelian anyon signatures, fusion rules, braiding, and the creation of hybrid Schrödinger cat states, with potential experimental applications.

Contribution

It demonstrates that cavity coupling can induce non-trivial topological phenomena and generate hybrid MZM-polariton cat states, providing new methods for manipulating topological quantum systems.

Findings

Evidence of non-trivial fusion rules and braiding operations.

Proposal for experimental probing via fermionic parity and Berry phases.

Generation of hybrid MZM-polariton Schrödinger cat states.

Abstract

We investigate the effects of coupling a local electromagnetic cavity to a segment of a topological Kitaev chain (KC), with particular emphasis on the interplay between photons and Majorana zero modes (MZMs). In addition to the well-known {\it scissor effect}-which effectively partitions the chain and isolates free MZMs in the bulk-we provide evidence of non-trivial fusion rules and braiding operations, hallmark signatures of non-Abelian anyons, enabled by spatially selective ultrastrong KC-cavity coupling. We propose that these distinctive MZM properties can be experimentally probed via fermionic parity measurements and photon-induced Berry phases. Furthermore, we demonstrate that, in the so-called sweet-spot regime, the coupled system can be mapped onto a Rabi-like model with a homodyne-rotated quadrature, offering a simplified yet powerful theoretical description. Exploiting the symmetry of fermionic modes within a two-site cavity configuration, we also show the feasibility of generating hybrid MZM-polariton Schr\"odinger cat states. Our findings offer a novel approach to manipulating topological quantum matter through local light-matter interactions and provide theoretical tools for future experimental realizations in platforms such as quantum materials or superconducting circuits.