Figure 1

The flux qubit ${\mathrm{NV}}^{-}$ spin ensemble hybrid system. (a) Photograph of the hybrid system from the top. A diamond crystal is bonded on top of the flux qubit chip with its (001) surface facing the chip. An in-plane magnetic field $B_{\mathrm{NV}}$ is applied in the [100] crystallographic axis. (b) Schematic of the flux qubit. The qubit consists of the main loop (lower red panel) and the $\alpha$ loop (upper blue panel) and four Josephson junctions (red crosses) characterized by Josephson energies $E_J$ and $\alpha E_J/2$. A typical $\alpha$ is about 0.9. ${\Phi }_{\epsilon }$ and ${\Phi }_{\alpha }$ are the magnetic flux through the main loop and the $\alpha$ loop, respectively. Two broadband lines on the qubit chip control them. A dc SQUID is attached to the qubit for readout of the qubit state (not shown) [20]. (c) Energy levels of the qubit as a function of a qubit flux ${\Phi }_{\mathrm{qb}}={\Phi }_{\epsilon }+{\Phi }_{\alpha }/2$. The energy imbalance $h\epsilon =2I_p{\Phi }_0({\Phi }_{\mathrm{qb}}/{\Phi }_0-1.5)$ between the two $I_p$ states can be controlled by ${\Phi }_{\mathrm{qb}}={\Phi }_{\epsilon }+{\Phi }_{\alpha }/2$. The energy splitting at the optimal point $h\Delta$ can be controlled solely by ${\Phi }_{\alpha }$, as shown by solid red curves and dotted blue curves. This enables us to couple the qubit to the ${\mathrm{NV}}^{-}$ center at the optimal point where the qubit has its longest coherence time. (d) Structure of an ${\mathrm{NV}}^{-}$ center in the diamond lattice. The red sphere is the vacancy, while the green sphere is the nitrogen atom. The black spheres are the three nearest neighbor carbon atoms. The NV axis can be along four equivalent $⟨111⟩$ directions, making the same angle of 55° with $B_{\mathrm{NV}}$ parallel to [100].Reuse & Permissions

Figure 2

Energy spectrum of the flux qubit ${\mathrm{NV}}^{-}$ spin ensemble hybrid system. (a) Transition frequency of an ${\mathrm{NV}}^{-}$ spin as a function of an in-plane magnetic field $B_{\mathrm{NV}}$. The dots represent the transition frequencies derived from the energy spectra of the flux qubit. Two curves are the results of the fitting to the Hamiltonian $H_{\mathrm{NV}}$ (see the main text). The parameters derived from the fitting are $D=2.878\mathrm{GHz}$ and $E=4\mathrm{MHz}$. (b) Energy spectrum of the flux qubit coupled to the ${\mathrm{NV}}^{-}$ spin ensemble under $B_{\mathrm{NV}}$ of 2.6 mT when the qubit splitting is tuned to $\Delta =2.84\mathrm{GHz}$. Here, $P_{\mathrm{sw}}$ is proportional to the population of the qubit excited state [26]. In the series of experiments, the qubit ground (excite) state leads $P_{\mathrm{sw}}=0(0.45)$. (c) Energy spectrum of the flux qubit coupled to the ${\mathrm{NV}}^{-}$ spin ensemble when $B_{\mathrm{NV}}=2.6\mathrm{mT}$ and $\Delta =2.92\mathrm{GHz}$. White curves represent transition frequencies of the hybrid system. The qubit is on resonance with the ${\mathrm{NV}}^{-}$ spin ensemble at point II, where we can perform an iswap operation based on a vacuum Rabi oscillation [20]. Changing ${\Phi }_{\mathrm{qb}}$ away from 1.5 ${\Phi }_0$ increases the detuning between them, resulting in the qubit being well decoupled from the spin ensemble at point I, where we perform qubit preparation, qubit detuning to store information in the memory, and qubit readout.Reuse & Permissions

Figure 3

Quantum memory operations. The inset in each figure shows the pulse sequence used in the operations, which is applied to the qubit through the on-chip control line for ${\Phi }_{\epsilon }$. I and II represent the operating points indicated in Fig. 2b. (a) Measurement results for the memory operation using a single quantum of energy. Red dots are the measured data with a green curve showing a fitted exponential decay with a decay time of $20.8\pm 0.7\mathrm{ns}$ (95% confidence interval). The memory operation begins by first preparing the qubit in the excited state $|1{⟩}_{\mathrm{qb}}$ using a microwave $\pi$ pulse (see the inset). An iswap gate transfers this excitation to the spin ensemble $|1{⟩}_{\mathrm{ens}}$, and the qubit is then detuned. The iswap gate consists of a shift pulse tuning the qubit on resonance with the spin ensemble, and its length is half of the period of a vacuum Rabi oscillation between them. The detuning between the qubit and the spin ensemble during its storage time $\tau$ is approximately 80 MHz. Finally, the information (the excitation) is retrieved back from the spin ensemble to the qubit using a second iswap gate followed by its measurement using a readout SQUID (the dashed red pulse indicates a current pulse applied to the SQUID for the readout). (b) Measurement results for the memory operation using the superposition state $(|0{⟩}_{\mathrm{ens}}+i|1{⟩}_{\mathrm{ens}})/\sqrt{2}$ with a detuning of approximately 70 MHz. Red dots are the measured data with the fitted green curve showing a decayed sinusoidal with a decay time of $33.6\pm 2.3\mathrm{ns}$ and a frequency of $70.4\pm 0.3\mathrm{MHz}$ (95% confidence interval). (c) Storing one qubit of an entangled state in the spin ensemble quantum memory. Red dots are the measured data with the green curve showing a fitting to Eq. (2). Fitting parameters are $\zeta =0.34$, $\delta \omega =87\mathrm{MHz}$, and $\varphi =0.85\mathrm{radians}$.Reuse & Permissions