Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
arXiv:2409.04515 · doi:10.1088/1402-4896/adf782
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 Schrödinger 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.
Main text: 18 pages, 7 Figures
References in corpus (32)
- Non-Abelian Anyons and Topological Quantum Computation
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- Quantum circuits with many photons on a programmable nanophotonic chip
- From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
- Anyons and the quantum Hall effect - a pedagogical review
- Superconducting Quantum Computing: A Review
- Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
- Realization of a minimal Kitaev chain in coupled quantum dots
- Cavity Quantum Materials
- Strongly-Correlated Electron-Photon Systems
- Parity qubits and poor man's Majorana bound states in double quantum dots
- Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths
- A two-site Kitaev chain in a two-dimensional electron gas
- Fate of photon blockade in the deep strong coupling regime
- Gauge Fixing for Strongly Correlated Electrons coupled to Quantum Light
- Drude weight, cyclotron resonance, and the Dicke model of graphene cavity QED
- Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
- Emulating quantum teleportation of a Majorana zero mode qubit
- Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
- Fusion protocol for Majorana modes in coupled quantum dots
- Signatures of Majorana protection in a three-site Kitaev chain
- Rényi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems
- Geometric phases in superconducting qubits beyond the two-level-approximation
- Observation of edge and bulk states in a three-site Kitaev chain
- Detecting Majorana Zero Modes via Strong Field Dynamics
- Majorana zero modes in Y-shape interacting Kitaev wires
- Parafermions in a multilegged geometry: Towards a scalable parafermionic network
- Majorana sweet spots in 3-site Kitaev chains
- From edge to bulk: Cavity induced displacement of topological non-local qubits
- Resonant Schrödinger Cat States in Circuit Quantum Electrodynamics
- Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling