Fast Room-Temperature Phase Gate on a Single Nuclear Spin in Diamond

Nuclear spins support long lived quantum coherence due to weak coupling to the environment, but are difficult to rapidly control using nuclear magnetic resonance as a result of the small nuclear magnetic moment. We demonstrate a fast $\sim 500\mathrm{ns}$ nuclear spin phase gate on a ${}^{14}\mathrm{N}$ nuclear spin qubit intrinsic to a nitrogen-vacancy center in diamond. The phase gate is enabled by the hyperfine interaction and off-resonance driving of electron spin transitions. Repeated applications of the phase gate bang-bang decouple the nuclear spin from the environment, locking the spin state for up to $\sim 140\mu \mathrm{s}$.

Figure 1

(a) Confocal image of the NV center used in the experiment. Two dc electrodes (not used) and a rf & MW stripline are fabricated near the NV center. Inset: Measurements of the second order correlation function $g^2(\tau )$, with $g^2(0)<0.5$ indicating emission from a single NV center. (b) Energy level diagram, with energy levels indexed by the electron spin quantum number $m_{\mathrm{I}}$ and nuclear spin quantum number $m_{\mathrm{S}}$. The $m_{\mathrm{S}}=+1$ level is not shown in the level diagram due to the relatively large electron Zeeman energy. Microwave excitations (MW1 and MW2) drive electronic transitions, while rf excitation is used to drive nuclear spin transitions. (c) Pulse sequence used to implement the nuclear spin phase gate during nuclear Rabi oscillations.

Figure 2

(a) PL measured as a function of rf frequency showing a nuclear spin transition at ${\nu }_{\mathrm{rf}}=2.934\mathrm{MHz}$, with a Gaussian fit to the data. (b) PL as a function of rf pulse length ${\tau }_{\mathrm{rf}}$ showing nuclear spin Rabi oscillations. (c) PL as a function of selective MW2 $\pi$-pulse frequency ${\nu }_{\text{MW}2}$ showing transition frequencies associated with the $m_I=+1$ and $m_I=0$ nuclear spin projections, with Gaussian fits to the data (see main text for details). (d) Nuclear Ramsey measurements: PL measured as a function of free precession time ${\tau }_{\text{free}}$ showing no visible decay out to $100\mu \mathrm{s}$.

Figure 3

(a) Nuclear Ramsey fringes with one phase gate of varying time $t$ applied $13\mu \mathrm{s}$ into the free-precession interval. Inset: Extracted phase shift of the fringes after the phase gate is applied. (b),(c) Comparison between bare nuclear Rabi oscillations (grey) and nuclear Rabi oscillations with fast $\pi$-phase gates applied (red): (b) One gate applied at $50\mu \mathrm{s}$. (c) Gates applied at $50\mu \mathrm{s}$ and $110\mu \mathrm{s}$. Red curves are simulation results.

Figure 4

Comparison between bare nuclear Rabi oscillations (grey) and nuclear Rabi oscillations with multiple $\pi$-phase gates applied in quick succession, locking the nuclear spin (red). Red curves are simulation results. (a) 5 gates applied every $5\mu \mathrm{s}$ from 20 to $40\mu \mathrm{s}$. (b) 35 gates applied every $4\mu \mathrm{s}$ from 20 to $156\mu \mathrm{s}$. (c) 6 gates applied every $4\mu \mathrm{s}$ from 30 to $50\mu \mathrm{s}$. (d) Nuclear Ramsey experiment with 11 $\pi$-phase gates applied at the times indicated by red arrows. In this case, there is no visible decrease in the amplitude of the Ramsey fringes. The theoretical prediction is given by the solid curve [20].