One- and Two-Dimensional Nuclear Magnetic Resonance Spectroscopy with a Diamond Quantum Sensor

We report on Fourier spectroscopy experiments performed with near-surface nitrogen-vacancy centers in a diamond chip. By detecting the free precession of nuclear spins rather than applying a multipulse quantum sensing protocol, we are able to unambiguously identify the NMR species devoid of harmonics. We further show that, by engineering different Hamiltonians during free precession, the hyperfine coupling parameters as well as the nuclear Larmor frequency can be selectively measured with up to five digits of precision. The protocols can be combined to demonstrate two-dimensional Fourier spectroscopy. Presented techniques will be useful for mapping nuclear coordinates in molecules deposited on diamond sensor chips, en route to imaging their atomic structure.

Figure 1

(a) Pulse protocol for conventional multipulse spectroscopy. Laser pulses are colored green, and microwave pulses are colored red. The $\pi$ pulse series used an $XY8$ phase pattern [20]. (b) Pulse protocol for a free nuclear precession measurement. The pulse marked by star was used for phase cycling (phases $Y$ and $\overline{Y}$). (c) Free-precession sequences exploited in our experiments and corresponding Hamiltonians ${\widehat{H}}_{\text{free}}^{(1\dots 3)}$. $t_1$ and $t_2$ are incremented evolution periods. The $\tau /2$ delays in ③ and ④ are used to adjust the axis of the nuclear Rabi rotation. (d) Sketch of the diamond chip with a near-surface NV center and ${}^{15}\mathrm{N}$, ${}^{13}\mathrm{C}$, and ${}^1\mathrm{H}$ nuclei. (e) Vectorial picture of the parallel and transverse hyperfine parameters $a_{||}$ and $a_{\perp }$. The contour represents a field line of the NV magnetic dipole.

Figure 2

Unambiguous identification of NMR signals: (a) Multipulse spectrum in a field of $B_0=174\mathrm{mT}$. Colors identify different data sets. (b)–(g) Fourier spectra for the six peaks labeled in (a). All spectra used Hamiltonian ${\widehat{H}}_{\text{free}}^{(1)}$, except for (d) and (e) that used ${\widehat{H}}_{\text{free}}^{(2)}$ [see Fig. 1]. The nuclear species and multipulse harmonic are indicated for each spectrum. The ${}^{15}\mathrm{N}$ peak is present due to a small misalignment of the external bias field.

Figure 3

(a) Multipulse spectrum and (b),(c) Fourier spectra at $\sim 8\mathrm{MHz}$. Two signals are present: one produced by the fundamental resonance of a ${}^1\mathrm{H}$ ensemble (b) and one produced by the second harmonic of a strongly coupled ${}^{13}\mathrm{C}$ nucleus (c). The third peak (star) in (a) is caused by the same ${}^{13}\mathrm{C}$ (data not shown). The number of pulses applied during ${\widehat{U}}_{\mathrm{CP}}$ was $N=1200$ in (a), 720 in (b), and 1000 in (c).

Figure 4

Precision measurement of ${\omega }_0$, $a_{||}$, and $a_{\perp }$ obtained by observing the nuclear, rather than the electronic, evolution. The same ${}^{13}\mathrm{C}$ as in Fig. 3 is being studied. (a) Free-precession signal under Hamiltonian ${\widehat{H}}_{\text{free}}^{(2)}$. (b) Fourier spectrum of (a) showing two peaks at ${\omega }_0$ and ${\omega }_0+a_{||}^{\prime }$. The enlargement on the upper peak shows a high-resolution spectrum obtained from an undersampled data set (see [22]), with $t_1$ up to $200\mu \mathrm{s}$. (Star) shows a traditional multipulse spectrum for comparison. Deduced parameters are ${\omega }_0/2\pi =2.09320(11)\mathrm{MHz}$ and $a_{||}^{\prime }/2\pi =4.02350(16)\mathrm{MHz}$ [22]. (c) Free-precession signal under Hamiltonian ${\widehat{H}}_{\text{free}}^{(3)}$. (Star) shows the corresponding multipulse signal obtained by incrementing the number of $\pi$ pulses $N=t_1/\tau$. (d) Fourier spectra of the two curves from (c). The deduced parameter is $a_{\perp }^{\prime }/2\pi =0.25070(41)\mathrm{MHz}$. Measurement uncertainties are fit errors [22].

Figure 5

Two-dimensional Fourier NMR spectrum (absolute value) of two ${}^{13}\mathrm{C}$ nuclei labeled by “$A$” and “$B$.” (a) is the measurement, and (b) is a simulation. The $f_1$ dimension plots ${\omega }_0+a_{||}^{\prime }/2$ and the $f_2$ dimension plots $a_{\perp }^{\prime }/\pi$. Dwell time was 120 ns (120 increments) for $f_1$ and 2168 ns (40 increments) for $f_2$. The peaks marked by star are present because the phase of the nuclear Rabi rotation was not perfectly adjusted. The total measurement time was 16 h.