Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on. These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting qubits.

Figure 1

Description of the hybrid quantum circuit demonstrated in this work. (a),(b) Three-dimensional sketch of the device and corresponding electrical scheme. The ensemble $N\mathrm{\text{−}}V$ of electronic spins (magenta) consists of ${10}^{11}$ NV centers in a diamond crystal glued on the chip surface. The transmon qubit $Q$ (in red) is capacitively coupled to a resonator $R$ (in blue) made nonlinear with a Josephson junction and used to readout its state. The bus $B$ (in yellow) is electrostatically coupled to $Q$ and magnetically coupled to $N\mathrm{\text{−}}V$. Bus $B$ contains a SQUID that makes its frequency ${\omega }_B(\Phi )$ tunable by applying in its loop a flux $\Phi$ via a fast on-chip current line $F$ (in green). A magnetic field $B_{\mathrm{NV}}$ is applied parallel to the [1,1,1] crystallographic axis. (c), (lower left inset) Energy level structure of NV centers. Transitions between $m_S=0$ and $m_S=\pm 1$ at frequency ${\omega }_{\pm }$ are further split in three resonance lines due to the hyperfine interaction with the ${}^{14}\mathrm{N}$ nuclear spin [20]. (main panel) Two-dimensional plot of the transmission $|S_{21}|(\omega ,\Phi )$ through $B$ in dB units, with $\Phi$ expressed in units of the superconducting flux quantum ${\Phi }_0=h/2e$, for a field $B_{\mathrm{NV}}=1.4\mathrm{mT}$ applied to the spins. Color scale goes from $-55\mathrm{dB}$ (background, green) to $-30\mathrm{dB}$ (magenta). Four vacuum Rabi splittings are observed whenever ${\omega }_B$ matches one NV center resonance frequency. The four transition frequencies ${\omega }_{\pm \mathrm{I},\mathrm{III}}$ correspond to the two distinct families $\mathrm{I}$ and $\mathrm{III}$ of NV centers, aligned along the [1,1,1] crystal direction parallel to $B_{\mathrm{NV}}$ or along one of the three other possible $⟨1,1,1⟩$ axes, respectively (see upper right inset). (main panel, bottom right) Qubit excited state probability $P_e$ as a function of the frequency of the exciting microwave and $\Phi$. Color scale goes from 0.1 (background, purple) to 0.3 (yellow). When ${\omega }_B$ matches the qubit frequency ${\omega }_Q=2.607\mathrm{GHz}$, the qubit spectrum shows an anticrossing demonstrating its coupling to $B$ with constant $g_Q/2\pi =7.2\mathrm{MHz}$.

Figure 2

Storage and retrieval of a single quantum of excitation from the qubit to the spin ensemble. (a), Experimental sequence showing the microwave pulses used for exciting the qubit in $|e⟩$ ($\pi$ pulse) and for reading it out ($R$ pulse), as well as transition frequencies of the quantum bus ($B$), qubit ($Q$), and spins ($N\mathrm{\text{−}}V$). (b), Experimental (red dots) and theoretical (black line—see text) probability $P_e(\tau )$ for ${\omega }_B$ tuned to ${\omega }_{-\mathrm{III}}$ (top) or ${\omega }_{-\mathrm{I}}$ (bottom), showing the storage and retrieval times ${\tau }_s$ and ${\tau }_r$. (c), Two-dimensional plot of $P_e$ versus interaction time $\tau$ and flux pulse height $\Phi$, showing resonance with the four spin groups. Chevron-like patterns are observed, showing a faster oscillation with reduced amplitude when ${\omega }_B$ is detuned from the spin resonance, as expected. Note that the difference between the ${\omega }_{-}$ and ${\omega }_{+}$ patterns in the same NV group is simply caused by the nonlinear dependence of ${\omega }_B$ on $\Phi$ [25].

Figure 3

Storage and retrieval of a coherent superposition of states from the qubit to the spin ensemble. (a) Experimental pulse sequence: the qubit is prepared by a $\pi /2$ pulse in state $(|g⟩+|e⟩)/\sqrt{2}$, which is transferred to $B$ by an $\mathrm{a}\mathrm{SWAP}$. Bus $B$ is then immediately tuned to ${\omega }_{-\mathrm{I}}/2\pi =2.84\mathrm{GHz}$ for an interaction time $\tau$. The quantum state of $B$ is then transferred back to the qubit by a second $\mathrm{a}\mathrm{SWAP}$. Quantum state tomography is finally performed to determine the qubit state by applying either $I$, $X$, or $Y$ operation to the qubit. (b), Trajectory of the qubit Bloch vector on the Bloch sphere (bottom inset), and its projection on the equatorial plane. (c), Modulus and phase of the off-diagonal element ${\rho }_{\mathrm{ge}}$ of the qubit density matrix as a function of interaction time $\tau$.

Figure 4

Ramsey-like experiment on the spin ensemble at the single-photon level. (a), Experimental pulse sequence: the qubit is prepared in its excited state $|e⟩$ by a $\pi$ pulse; the state $|e,0_B⟩$ is then adiabatically transferred to $|g,1_B⟩$ by an $\mathrm{a}\mathrm{SWAP}$. A fast flux pulse subsequently brings ${\omega }_B$ onto ${\omega }_{-\mathrm{I}}$, and then lets $B$ and the spins from group $-\mathrm{I}$ interact for half a swap time ${\tau }_{\pi /2}={\tau }_{s,\mathrm{I}}/2$, generating an entangled state of the two systems. $B$ is then detuned from the spins by $\delta \omega /2\pi =38\mathrm{MHz}$ during a time $\tau$, and a second half-swap is performed. The quantum state of $B$ is then transferred back to the qubit, which is finally readout. (b), Measured (red circles) and calculated (black line—see text) probability $P_e(\tau )$, as well as the Fourier transform of the experimental data (inset) revealing the NV centers HF structure.