Strongly coupled diamond spin qubits by molecular nitrogen implantation

Ionized nitrogen molecules (${}^{15}$N${}_2^{+}$) are used as efficient point sources for creating NV${}^{-}$ pairs in diamond with nanoscale spatial separation and up to 55 kHz magnetic coupling strength. Co-implantation of ${}^{12}$C${}^{+}$ increased the yield of pairs, and a ${}^{13}$C-depleted diamond allowed 0.65 ms coherence times to be obtained. Further coupling to a third dark spin provided a strongly coupled three-spin register. These results mark an important step towards realization of multiqubit systems and scalable NV${}^{-}$ quantum registers.

Figure 1

Simulation of spatial distribution for ${}^{15}$N ions and vacancies. (a) Simulated depth distribution of implanted ${}^{15}$N atoms with 10 keV energy (solid circles), Gaussian fit (solid line), distribution of vacancies arising from ${}^{15}$N implantation (dashed line), and distribution of vacancies from 20 keV ${}^{12}$C co-implantation (dot-dashed line). (b) Simulated probability distribution of distance between two ${}^{15}$N atoms arising from the same N${}_2$ implanted molecule (solid circles), and the resultant dipolar coupling between two NV${}^{-}$ centers with this separation (solid line). Note that we averaged the angular component in the dipolar coupling of ${\nu }_{\mathrm{dip}}=\frac{3}{2}{D}_{\mathrm{dip}}\overline{|3{\cos }^2\theta -1|}$ where $\theta$ is the angle between the vector r connecting two dipoles and the magnetic field, and the dipolar coupling constant $D_{\mathrm{dip}}\sim 5.2\times {10}^{-23}/r^3$ kHz. (c) Calculated fidelity of $\exp [-{\left(\frac{1}{{\nu }_{\mathrm{dip}}{T}_2}\right)}^2]$ for a two-qubit entanglement with various coherence times $T_2$.

Figure 2

Confocal microscopy of NV${}^{-}$ centers. (a) A fluorescence confocal image of the co-implanted (${}^{15}$N${}_2$ and ${}^{12}$C implanted) region with an area of $25\times 25$ $\mu$m${}^2$ (left). Bright yellow dots correspond to NV centers. The coordinate mapping of ODMR identified ${}^{14}$NV${}^{-}$ (cross), ${}^{15}$NV${}^{-}$ (solid circle), and ${}^{15}$NV${}^{-}$-${}^{15}$NV${}^{-}$ pairs (open circle) is shown in the right figure. (b) A fluorescence confocal image of the ${}^{15}$N${}_2$-only implanted region with an area of $25\times 25$ $\mu$m${}^2$ (left) and the coordinate mapping (right) showing ${}^{15}$NV${}^{-}$ (solid circle) and an ${}^{15}$NV${}^{-}$-${}^{15}$NV${}^{-}$ pair (open circle).

Figure 3

Dipolar coupling of a ${}^{15}$NV${}^{-}$ pair measured by DEER. (a) Illustration of NV pair creation by N${}_2^{+}$ molecular ion implantation. (b) Measured spin echo data for the ${}^{15}$NV${}^{-}$ pair are fitted with $E\left(2\tau \right)=a+b\exp [-{(2\tau /T_2)}^{\alpha }]$ showing long $T_{2,\mathrm{HE}}$ times of 0.65 ms ($\alpha =1.14$) and 0.63 ms ($\alpha =1.31$). (c) DEER pulse sequence with NV${}_{\mathrm{J}}$ as sensor and NV${}_{\mathrm{K}}$ as emitter. (d) ODMR spectrum of the investigated NV pair shows the selective addressability of the two ${}^{15}$NV${}^{-}$ centers due to their different axis orientation, where a magnetic field of $\sim$34 G parallel to NV${}_{\mathrm{J}}$ axis. (e) The resulting echo modulation on NV${}_{\mathrm{J}}$ shows a coupling strength of 55 kHz.

Figure 4

Ramsey measurements on a coupled ${}^{15}$NV${}^{-}$ pair and third dark spin. (a) Hyperfine spin transitions between $m_{\mathrm{s}}=0,-1$ states for NV${}_{\mathrm{J}}$. A magnetic field of $\sim$46 G was applied parallel to NV${}_{\mathrm{J}}$. The detuning frequency (${\nu }_0$) used for the $\pi /2$ pulses in the Ramsey sequence is indicated by the arrow. (b) The alternating Ramsey sequence. Two different ground states, GS${}_{\mathrm{emitter}}$, of $|0\rangle$ and $|-1\rangle$ are prepared without and with a $\pi$ pulse on the emitter spin, respectively. (c) Experimental data of the Ramsey pulse sequence, showing a $T_2^{*}$ for NV${}_{\mathrm{J}}$ of 100 $\mu$s. A vertical offset for the data with (black) and without (gray) the $\pi$ pulse on the emitter spin was added for pictorial clarity. (d) The FFT of the obtained Ramsey data, showing a shift of 55 kHz for the two different states of the emitter NV and also an additional splitting from the expected frequencies (dot-dashed lines) of 172 kHz.