Generating maximally-path-entangled number states in two spin ensembles coupled to a superconducting flux qubit

An ensemble of nitrogen-vacancy (NV) centers coupled to a circuit QED device is shown to enable an efficient, high-fidelity generation of high-N00N states. Instead of first creating entanglement and then increasing the number of entangled particles $N$, our source of high-N00N states first prepares a high-$N$ Fock state in one of the NV ensembles and then entangles it to the rest of the system. With such a strategy, high-$N$ N00N states can be generated in just a few operational steps with an extraordinary fidelity. Once prepared, such a state can be stored over a longer period of time due to the remarkably long coherence time of NV centers.

Figure 1

(a) Two ensembles of NV centers coupled to a superconducting flux qubit consisting of four Josephson junctions forming the main loop and an $\alpha$ loop. (b, c) Crystal-lattice (b) and energy (c) diagrams of an NV center in diamond.

Figure 2

N00N state generation in NVE memories: $U,$ time evolution of a quantum state, governed by the time-evolution operator $U\left(t\right)=e^{-i{H}_{\mathrm{eff}}\mathrm{\Delta }t/\hslash }$ with the effective Hamiltonian $H_{\mathrm{eff}}$; $\mathcal{H}$, an Hadamard gate acting locally on the flux qubits. Within the time interval $\mathrm{\Delta }{t}_1=\pi /\left(4\mathrm{\Omega }\right)$, the system evolves from its specifically tailored initial state to ${|\psi \rangle }_1$. The Hadamard transform yields the state ${|\psi \rangle }_2$. Upon a measurement on the state of the flux qubit, the total wave function of the systems collapses to ${|\psi \rangle }_3$. At the final step, time evolution $U\left(t\right)$ creates the desired N00N state.

Figure 3

Time evolution of the density matrix elements ${\rho }_{ij,kl}$ (a) and the fidelity (b) calculated by solving Eq. (12) for the NVE-flux-qubit source of N00N states with an $N=2$ N00N state prepared in a system at $t=0$.