Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators

We propose a potentially practical scheme to entangle negatively charged nitrogen-vacancy (N-$V$) centers in distant diamonds. Each diamond is supposed to be fixed on the exterior surface of a microtoroidal resonator, and the single-photon input-output process—a currently available technique—could entangle separate N-$V$ centers in a scalable fashion. The feasibility of our scheme and the experimental challenge are discussed by considering currently available techniques for qualified N-$V$ centers and cavities.

Figure 1

Schematic setup to generate entanglement between electron spins of two remote N-$V$ centers fixed on the exterior surface of MTRs via a single photon input and output, where the inset shows the configuration of the N-$V$ center under an external magnetic field with two of the levels driven resonantly by the input $L$-polarized single photon (the dotted line). The dashed line represents the coupling by $R$-polarized radiation, which does not happen in the present scheme due to large detuning. The bold lines mean the levels encoding qubits and ${\gamma }_e$, the electron gyromagnetic ratio.

Figure 2

Reflectance against cavity damping at ${\omega }_c={\omega }_0={\omega }_p$ with (a) showing $r({\omega }_p)~1$ in the case of $\Omega ⩾5\sqrt{\kappa \gamma }$ and for (b) $Q={10}^4$ and $Q={10}^5$ corresponding to the blue solid and red dashed lines, respectively.

Figure 3

Reflectance and phase shift of the reflection coefficient $r({\omega }_p)$ as functions of the detuning between the input single-photon pulse and the WGM with (a), (b) $\kappa =2\pi \times 10$ GHz and with (c), (d) $\kappa =2\pi \times 1$ GHz. The solid curves in orange are for $r_0(\omega )$ with $\Omega =0$, and the dashed curves in blue represent $r(\omega )$ with $\Omega =2\pi \times 500$ MHz and ${\omega }_0={\omega }_c$.