Identification and Control of Electron-Nuclear Spin Defects in Diamond

We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. Finally, we create quantum coherence among the three electron spins, paving the way for the creation of genuine tripartite entanglement. This approach will be useful in assembling multispin quantum registers for applications in quantum sensing and quantum information processing.

Figure 1

Identifying two unknown spin defects in diamond. (a) A single nitrogen-vacancy center (NV) interacts with two electron-nuclear spin defects ($X_1$, $X_2$) in diamond. The spin-echo double-resonance (SEDOR) spectrum measured by applying a recoupling $\pi$ pulse at a variable frequency ${\overrightarrow{\nu }}_{\mathrm{X}}$ during a spin-echo on the NV electron spin exhibits two resolved hyperfine doublets centered around the free-electron spin resonance frequency ${\nu }_e={\gamma }_e{B}_0$, where ${\gamma }_e$ is the gyromagnetic ratio of the free electron and $B_0=171.8\mathrm{G}$ is the strength of the static magnetic field oriented along the molecular axis of the NV center. The solid line is a fit to four Lorentzian spectral lines associated with the two hyperfine resonances of $X_1$ (blue, outer spectral lines) and $X_2$ (green, inner spectral lines) (b) The unknown parameters of the hyperfine and dipolar tensors of the $X$ spins are measured by varying the strength and orientation of the magnetic field using a permanent magnet. The polar and azimuthal angles parametrizing the orientation of the magnetic field ($\theta$, $\varphi$) and the principal axes of the hyperfine tensors for the NV center (${\theta }_{\mathrm{NV}}=54.7°$, ${\varphi }_{\mathrm{NV}}=0°$) and $X$ spins (${\alpha }_X$, ${\beta }_X$) are defined with respect to the crystallographic axes (${\mathbf{x}}_C,{\mathbf{y}}_C,{\mathbf{z}}_C$) of the diamond crystal. (c) NV resonance frequency for various magnet positions. For each magnet position, there exist multiple values of the strength and orientation of the magnetic field that result in the same NV resonance frequency (inset). (d) Electron-spin-echo envelope modulation (ESEEM) spectroscopy of the NV center for various magnet positions. The spectral components at the nuclear frequencies result from hyperfine mixing with the host ${}^{15}\mathrm{N}$ nuclear spin in the presence of a nonaxial magnetic field. For each magnet position, the field strength ($B_0$) and polar angle ($\theta$) are unambiguously determined by finding the simulated spectrum (dotted lines) that best matches the measured spectrum. The frequency wrapping for large magnet positions is an artifact of bandlimited sampling that is captured by our model.

Figure 2

Characterizing the hyperfine tensors of two spin defects in diamond. (a) Measured hyperfine strengths for various polar angles of the magnetic field ($\theta$) plotted with respect to the polar angle of the NV center (${\theta }_{\mathrm{NV}}$) in the azimuthal plane $\varphi =0°$. (b) Measured hyperfine strengths for various azimuthal angles of the static magnetic field ($\varphi$) in the polar plane $\theta =90°$. The solid lines are the curves of best least-square fit of both sets of data to the eigenvalues of an axially symmetric hyperfine tensor with four free parameters.

Figure 3

Locating two spin defects in diamond. (a) Typical dipolar oscillations measured using a recoupled spin-echo sequence in the presence of a nonaxial magnetic field. The slow modulation (solid blue line) is caused by the dipolar interaction between the NV electron spin and the $X_1$ electron spin, whereas the fast modulation is caused by the hyperfine mixing with the NV nuclear spin. (b) Measured dipolar coupling strengths between the NV electron spin and the $X_1$ (blue) and $X_2$ (green) electron spins for various magnet positions. The solid line is the best least-square fit to the eigenvalues of the interacting spin Hamiltonian with three free parameters ($r$, $\zeta$, $\xi$, see [34]), which parametrize the relative position of the two $X$ spins with respect to the NV center. (c) and (d) Probability distribution maps of the location of the $X_1$ (top) and $X_2$ (bottom) spins defined with respect to the coordinate frame of the NV center placed at the origin. The darker color indicates a higher probability of finding the $X$ spin at this specific location.

Figure 4

Creating and detecting three-spin coherence. (a) and (b) The dissipative channel $\mathrm{\Phi }$ removes entropy out of the quantum system by optically pumping the NV center (green box). The swap gates implemented using Hartmann-Hahn cross polarization with $\pi /2$ pulses along the $\pm y$ axis (bright and pale red box) and continuous driving along the $\pm x$ axis (bright and pale blue box) exchange the state of the NV and $X$ spins, effectively polarizing the $X$ spins. A series of Hadamard ($H$) and cnot gates implemented using $\pi /2$ and $\pi$ pulses realize an entangling and disentangling gate to create and detect three-spin coherence, which is protected against dephasing by a series of $X$ gates. The three-spin coherence is mapped back into a population state of the NV spin using a series of disentangling gates and measured projectively in the $Z$ basis (green box). The phase of the pulses of the disentangling gate on the NV, $X_1$, and $X_2$ spins are incremented by steps of $\mathrm{\Delta }{\varphi }_{\mathrm{NV}}=5\pi /10$, $\mathrm{\Delta }{\varphi }_2=2\pi /10$, and $\mathrm{\Delta }{\varphi }_1=\pi /10$, respectively, to spectrally label the spin coherence terms. (c) The power spectrum of the signal shows parity oscillations [50] at the sum of the three modulation rates ($\mathrm{\Delta }{\varphi }_{\mathrm{\Sigma }}=8\pi /10$), thus, indicating the creation of three-spin coherence [34].