Entanglement of nitrogen-vacancy-center ensembles using transmission line resonators and a superconducting phase qubit

We propose a potentially practical scheme for creating entanglement between two distant nitrogen-vacancy-center (N-$V$) spin ensembles using a current-biased Josephson junction superconducting qubit and transmission line resonators. The idea provides a scalable way to an N-$V$ ensemble-based quantum network, which is close to the reach with currently available technology.

Figure 1

(a) The coupled system of a CBJJ and two TLRs, where the CBJJ acts as a tunable coupler between the two TLRs. The TLR1 and TLR2 are interconnected by a CBJJ from left and right by the coupling capacitors $C_c$. The NVEs are coupled via the common quantized field of the superconducting TLR cavity, which acts as a quantum bus. (b) Electronic model of the CBJJ. When the bias current $I_b$ is driven close to the critical bias $I_c$, there exist only a few bound states $|n\rangle {}_C$ with energy $E_n$ in each washboard well (see text for more details). (c) Level structure of single N-$V$ center, where the electronic ground and first excited states are electron spin triplet states (S = 1), and $D_{\mathit{gs}}/2\pi =2.87$ GHz is the zero-field splitting between the lowest energy sublevels $m_s=0$ and $m_s=\pm 1$.

Figure 2

The fidelity $F_B$ of the NVE-qubit maximum entangled states $|\Psi {\rangle }_{\mathrm{Bell}}^{(+)}$, where we have set operating time $t_{\mathrm{op}}^{\text{'}}=4\pi /{\Omega }^{\text{'}}$. (a) The fidelity $F_B$ versus the parameter ${\delta }^{\text{'}}$ and the decay rate ${\kappa }_c$. (b) The fidelity $F_B$ versus the parameter ${\delta }^{\text{'}}$ in the case of ${\kappa }_c=0.02g^{\text{'}}$ (dotted line), ${\kappa }_c=0.08g^{\text{'}}$ (solid line), and ${\kappa }_c=0.1g^{\text{'}}$ (dashed line), respectively. (c) The fidelity $F_B$ versus the parameter $g^{\text{'}}t$ and the parameter ${\delta }^{\text{'}}$, where ${\kappa }_c=0.1g^{\text{'}}$. (d) The fidelity $F_B$ versus the parameter $g^{\text{'}}t$ in the case of ${\delta }^{\text{'}}=1.2$ (dotted line), ${\delta }^{\text{'}}=1.3$ (solid line), and ${\delta }^{\text{'}}=1.4$ (dashed line), respectively, where ${\kappa }_c=0.1g^{\text{'}}$.