Entanglement between an NV Center and Chiral Photons in a Topological SWCNT Plasmonic Microtoroid

We present a theoretical proposal for a hybrid solid-state quantum node based on a single nitrogen-vacancy (NV) center coupled to a topological single-walled carbon nanotube (SWCNT) plasmonic microtoroid. The SWCNT ring supports deeply sub-wavelength whispering-gallery-like plasmonic modes that are naturally described within a Tomonaga-Luttinger liquid framework. Owing to the closed-ring topology, the cavity spectrum contains a zero-mode sector that is tunable by an external magnetic flux through an Aharonov-Bohm shift. We show that the strongly confined CNT near field can exhibit chiral spin-momentum locking, enabling the two circularly polarized NV transitions to couple selectively to clockwise and counter-clockwise cavity modes, while the parasitic linearly polarized π-transition is strongly suppressed by the pronounced anisotropy of the local Purcell enhancement. Based on a tripod stimulated Raman adiabatic passage (STIRAP) scheme, the system can in principle map the NV spin onto a spin-photon entangled state in a deterministic manner, which is then emitted into a side-coupled tapered optical fiber as a tunable flying qubit. We derive the cavity spectrum, the chiral selection rules, the effective tripod Hamiltonian, and the open-system master equation. Quantitative estimates indicate that, under cryogenic conditions and in the overcoupled regime, high-fidelity spin-photon entanglement and in situ magnetic tuning of the emitted photon frequency are in principle achievable. We also discuss a realistic fabrication route for the CNT resonator and deterministic positioning strategies for a single NV center in the CNT near field.