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

Abstract

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.

Figures (3)

• Figure 1: Proposed hybrid quantum node and relevant NV-level structure. (a) Schematic of the hybrid system. A closed SWCNT ring supports strongly confined plasmonic whispering-gallery-like modes. A perpendicular magnetic field $\mathbf{B}$ threads the ring and generates an Aharonov-Bohm flux $\Phi$, thereby tuning the cavity resonance $\omega_c(\Phi)$Ando1993Bachtold1999. A nearby NV center couples to the chiral cavity field with coupling strength $g$. The cavity is side-coupled to a tapered optical fiber with external decay rate $\kappa_{\mathrm{ex}}$, enabling collection of the emitted flying photonic qubit. (b) Relevant NV-center level scheme used in the tripod-STIRAP protocol. The ground-state spin sublevels are $|0\rangle$ and $|\pm1\rangle$, and the optically excited state is $|A_2\rangle$. A classical pump field with Rabi frequency $\Omega_p(t)$ drives the $|0\rangle\leftrightarrow|A_2\rangle$ transition, while the two circularly polarized transitions $|A_2\rangle\leftrightarrow|-1\rangle$ and $|A_2\rangle\leftrightarrow|+1\rangle$ couple selectively to the CW and CCW cavity modes, respectively. The linearly polarized $\pi$ channel associated with $|A_2\rangle\leftrightarrow|0\rangle$ is assumed to be strongly suppressed in the chiral CNT near field.
• Figure 2: Illustrative dynamics and parameter dependence of the tripod protocol. (a) Population dynamics during adiabatic Raman transfer from the initial state $|0,\mathrm{vac}\rangle$ to the two target states $|-1,1_{+},0_{-}\rangle$ and $|+1,0_{+},1_{-}\rangle$, with only weak transient occupation of the excited state $|A_2\rangle$. Here $|\mathrm{vac}\rangle\equiv|0_{+},0_{-}\rangle$ denotes the two-mode cavity vacuum. (b) Dependence of the total emission fidelity on the intrinsic cavity loss rate $\kappa_0$ for different values of the spontaneous decay rate $\gamma$. The upper envelope is set by the extraction efficiency $\eta_{\mathrm{ext}}=\kappa_{\mathrm{ex}}/(\kappa_{\mathrm{ex}}+\kappa_0)$.
• Figure 3: Parameter-scaling plots for the emitter--CNT vacuum coupling $g$ and the maximum fiber outcoupling rate $\kappa_{\mathrm{ex}}^{\max}$. The panels illustrate general scaling trends rather than a fully optimized device design for a specific emitter platform. (a) Distance dependence of the single-photon vacuum Rabi coupling $g$, showing the near-field decay $g(x)\propto \exp(-x/L_d)$. Parameters: $\omega_c/2\pi=193\,\mathrm{THz}$, $|\mathbf{d}|=10\,\mathrm{Debye}$, $\epsilon_r=1$, $L_d=5\,\mathrm{nm}$, and $V_{\mathrm{mode}}=1.5\times10^{-22}\,\mathrm{m^3}$. (b) Mode-volume dependence $g(V_{\mathrm{mode}})\propto V_{\mathrm{mode}}^{-1/2}$ at a fixed separation $x=10\,\mathrm{nm}$, using the same parameters as in (a). (c) Radius dependence of the maximum external coupling rate $\kappa_{\mathrm{ex}}^{\max}\equiv\kappa_R$, illustrating the scaling $\kappa_R\propto R$ for fixed fiber parameters. Parameters: cavity wavelength $\lambda_c=1550\,\mathrm{nm}$, $\xi=0.2$, $A_{\mathrm{eff}}^{\mathrm{CNT}}=10^{-17}\,\mathrm{m^2}$, $A_{\mathrm{eff}}^{\mathrm{Fiber}}=10^{-14}\,\mathrm{m^2}$, and $L_{\mathrm{int}}=0.20\,\mu\mathrm{m}$. (d) Dependence of $\kappa_{\mathrm{ex}}^{\max}$ on the fiber effective mode area, showing the mismatch-limited scaling $\kappa_{\mathrm{ex}}^{\max}\propto (A_{\mathrm{eff}}^{\mathrm{Fiber}})^{-1}$ at fixed $R=2\,\mu\mathrm{m}$, with the other parameters the same as in (c). All rates are plotted as $g/2\pi$ and $\kappa_{\mathrm{ex}}^{\max}/2\pi$ in GHz.