Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States

• URL: http://arxiv.org/abs/2409.04515v2
• Date: Thu, 28 Aug 2025 10:13:36 GMT
• Title: Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Authors: Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor,
• Abstract summary: We investigate the effects of coupling a local electromagnetic cavity to a segment of a topological Kitaev chain (KC)<n>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.<n>Our findings offer a novel approach to manipulating topological quantum matter through local light-matter interactions.
• Score: 36.94429692322632
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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