Unambiguous nuclear spin detection using an engineered quantum sensing sequence

Sensing, localizing, and identifying individual nuclear spins or frequency components of a signal in the presence of a noisy environment requires the development of robust and selective methods of dynamical decoupling. An important challenge that remains to be addressed in this context are spurious higher-order resonances in current dynamical decoupling sequences as they can lead to the misidentification of nuclei or of different frequency components of external signals. Here we overcome this challenge with engineered quantum sensing sequences that achieve both enhanced robustness and the simultaneous suppression of higher-order-harmonic resonances. We experimentally demonstrate the principle using a single nitrogen-vacancy center spin sensor which we apply to the unambiguous detection of external protons.

Figure 1

Robust quantum sensing sequences for single nuclear spin detection. (a) XY8 pulse sequence consisting of repetitive $\left[{\left(\pi \right)}_x{\left(\pi \right)}_y{\left(\pi \right)}_x{\left(\pi \right)}_y{\left(\pi \right)}_y{\left(\pi \right)}_x{\left(\pi \right)}_y{\left(\pi \right)}_x\right]$ pulses and (b) YY8 pulse sequence consisting of $\left[{\left(\pi \right)}_{-y}{\left(\pi \right)}_y{\left(\pi \right)}_y{\left(\pi \right)}_{-y}{\left(\pi \right)}_{-y}{\left(\pi \right)}_{-y}{\left(\pi \right)}_y{\left(\pi \right)}_y\right]$ pulses where each bar refers to a $\pi$ rotation around the $\pm \widehat{x},\pm \widehat{y}$ axis (with $t_{\pi }$ the pulse duration). (c), (d) A field with a frequency of ${\omega }_{\text{second}}={\omega }_L/2$ and ${\omega }_{\text{fourth}}={\omega }_c/4$, where ${\omega }_c=1/\left(2\tau \right)$ with $\tau$ the interpulse time interval, may lead to a spurious high-order resonance signal.

Figure 2

The spectrum signal of the ${}^{13}\mathrm{C}$ nuclear spins observed by a NV center using XY8-1 and YY8-1 pulse sequences with different initial phases $\varphi =0$ ($\circ$), $\pi /2$ ($\diamond$), and $\pi$ ($\square$). The Rabi frequency is $\mathrm{\Omega }=\left(2\pi \right)25\mathrm{MHz}$ and the magnetic field is $510\mathrm{G}$.

Figure 3

Suppression of spurious high-order resonance signals using engineered quantum sensing pulse sequences. (a), (b) The second- and fourth-harmonic responses using the XY8-6 and XY8-12 pulse sequences with the initial phase $\varphi =\pi /6$ ($\circ$) and $3\pi /4$ ($\square$), respectively. (c) The amplitude of the second- ($\square$) and fourth- ($\diamond$) harmonic signal (i.e., the resonance contrast) as a function of the initial phase using the XY8-6 and XY8-12 pulse sequences. (d), (e) The second- and fourth-harmonic response using the YY8-6 and YY8-12 pulse sequences with the initial phase $\varphi =0$ ($\square$) and $\pi /2$ ($\circ$), respectively. (f) The amplitude of the second- ($\square$) and fouirth- ($\diamond$) harmonic signal as a function of the initial phase using the YY8-6 and YY8-12 pulse sequences. The Rabi frequency is $\mathrm{\Omega }=\left(2\pi \right)25$ MHz. Both spurious harmonics can be suppressed simultaneously for YY8 pulse sequences which contrasts with XY8 pulse sequences.

Figure 4

Detection of ${}^1\mathrm{H}$ magnetic resonance signal using the YY8 pulse sequence. (a) The spectrum as measured by a shallow NV center spin for various magnetic fields. (b) The frequency of peak response as a function of the magnetic field $B$. The red line has a slope $4.20\pm 0.13$ kHz/G that gives an estimated gyromagnetic ratio of ${}^1\mathrm{H}$. The Rabi frequency is $\mathrm{\Omega }=\left(2\pi \right)25$ MHz.