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arXiv · 2409.04515

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

Luis Quiroga·Fernando J. Gómez-Ruiz·Ivan A. Bocanegra-Garay·Ferney J. Rodríguez·Carlos Tejedor
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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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Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor. 2024-09-06. Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schr\"odinger Cat States. https://doi.org/10.1088/1402-4896/adf782

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