TOPOLOGICAL QUBITS & PHOTONS: ANYONS AND MAJORANA-SCHRÖDINGER CAT STATES

"The search for new materials that show strong light-matter interaction is a very active field that has evolved from a theoretical idea to an experimental reality. When the interaction is stronger than the dissipation of light and matter entities (ultra-strong coupling regime), typically by embedding materials into resonators (QED regime), the formation of hybrid half-light half-matter bosonic quasiparticles called polaritons becomes possible. In this talk, we report on the impact of a local microcavity at the center of a topological chain, revealing profound effects on the system's quantum states. Notably, acting as a localized quantum impurity, the cavity produces a scissor-like effect releasing Majorana zero modes (MZMs) within the matter bulk [1]. This setup enables the observation of non-trivial fusion rules and braiding --key signatures of non-Abelian anyons-- facilitated by the spatially selective ultra-strong coupling to the cavity photon field. These MZM statistical features can be directly probed through fermionic parity readouts and photon Berry phases, respectively. Furthermore, by leveraging the symmetry properties of fermion modes within a two-site cavity, we propose a novel method for generating MZM-polariton Schrödinger cat states [2]. Finally, perspectives on the control of topological quantum systems, offering new avenues for both fundamental research and potential quantum computing applications, will be discussed. [1] F. P. M.Méndez-Córdoba, J.J.M-A., F.J.G-R., F.J.R., C.T. and L.Q., From edge to bulk: cavity-induced displacement of topological nonlocal qubits , Physical Review B107, 125104 (2023). [2] L.Quiroga, F.J.G-R., I.A.B-G., F.J.R. and C.T, Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States, arxiv:cond-mat/2409.04515"