Enhanced sensitivity in microscale high-field NMR via nuclear-spin locking with NV centers

TL;DR

This work addresses the challenge of sensing high-frequency NMR signals at high magnetic fields using NV centers by introducing continuous-AERIS, a spin-locking–based amplitude-encoded protocol. By replacing free nuclear evolution with weak RF spin locking, the nuclear coherence time is extended from $T_2^*$ to $T_{1\rho}$, enabling longer, more robust signal acquisition and substantially improved sensitivity (≈4×) without sacrificing essential chemical information. The approach preserves and recovers chemical shifts and $J$-couplings, even in the presence of heteronuclear and homonuclear couplings, while accounting for repolarization overhead and driving errors. Together, these results demonstrate a practical path toward faster, higher-sensitivity microscale NMR at high fields using NV-based sensors, with robust strategies for driving imperfections and potential extensions to pure-shift-like spectra.

Abstract

Solid state defects such as nitrogen vacancy (NV) centers in diamond have been utilized for NMR sensing at ambient temperatures for samples at the nano-scale and up to the micro-scale. Similar to standard NMR, NV-sensitivities can be increased using tesla-valued magnetic fields to boost nuclear thermal polarization, while structural parameters, such as chemical shifts, are also enhanced. However, with standard microwave (MW) based sensing techniques, NV centers struggle to track fast megahertz Larmor frequencies encountered in high-field scenarios. Previous protocols have addressed this by mapping target NMR parameters to the signal amplitude rather than the frequency, using a mediating RF field. Although successful, protocol sensitivities are limited by the coherence time ($T_2^*$) of the NMR signal owing to the presence of stages where the sample magnetization freely evolves. In this work, we propose extending this coherence time, and consequently improving sensitivity, via amplitude encoding with weak nuclear spin locking instead of free evolution, thereby taking advantage of the longer sample coherence times ($T_{1ρ}$). We demonstrate this can enhance protocol sensitivities by $\gtrsim 4$ times.

Figures (6)

• Figure 1: A schematic of an NV based microscale NMR sensor. An ensemble of NV centers sense the NMR signal generated by a bubble of molecules in a liquid on the surface of the diamond. The bubble has a radius proportional to the depth of the NV centers targeted by laser irradiation. Although the number of molecules is generally constant, molecules can diffuse in and out. Manipulation of this NMR signal can be performed by applying RF driving resonant with the target nuclei, for example $^1$H. Measurement and analysis of the NMR signal is performed on the collected photons from the fluorescence of the NV centers after applying MW pulse sensing protocols.
• Figure 2: Simulations of the NMR signal generated by hydrogen nuclei in a sample of methyl acetate ($\mathrm{C}_3\mathrm{H}_6\mathrm{O}_2$) under RF manipulation. (a) The simulated NMR signal generated by the hydrogen nuclei at $B_0 = 2 \,\mathrm{T}$ is numerically simulated by combining single molecule signal for $10^4$ separate realizations, each with a unique noise trajectory sampled from an OU process with $\sigma/2\pi = 10\,\mathrm{Hz}$ and $\tau_c = 4.6\,\mathrm{ms}$. For FID (orange), the NMR signal is shown to decay with a coherence time $T^*_2 \simeq 60\mathrm{ms}$, whereas by applying a RF driving in the $x$-$y$ plane with $\Omega_1/2\pi = 1\,\mathrm{kHz}$ (purple), the coherence time of the signal increases significantly to $T_{1\rho}\simeq 600\,\mathrm{ms}$. In the inset, a Fourier transform of the signal illustrates the characteristic chemical shifts for methyl acetate $(\delta _a,\delta_b)= (2.05,3.662)\,\mathrm{ppm}$ for FID and Fourier peaks enhanced by a factor of approximately 4 under RF driving at shifts predicted by Eq.(\ref{['Eq: NSLsignal']}). (b) Increasing coherence times for large Rabi frequencies are shown, albeit with increasingly small chemical shifts to sense, where $T_{1\rho}$ (purple) increases indefinitely. We also plot $\tilde{T}_\mathrm{1\rho} = 1/(1/T_1 + 1/T_{1\rho})$ (gray), where $T_1 \sim 1.5\,\mathrm{s}$ is a decay time through a different mechanism. Including this, the effective decay time converges to $\tilde{T}_\mathrm{1\rho} = 1.5\,\mathrm{s}$.
• Figure 3: A schematic for our protocol --continuous-AERIS-- and simulated spectra of three chemical compounds. (a) A pictorial demonstration of how to execute the protocol. A $\pi/2$ RF pulse incident on the target nuclei initializes their net magnetization into the $x$-$y$ plane. Unlike standard AERIS methods, a low amplitude RF driving ($\Omega_1/2\pi = 1.0 \,\mathrm{kHz}$) is applied in the encoding stage to perform a $2\pi n_1$ rotation. Due to the low amplitude, any detuning from the Larmor frequency owing to chemical shifts $\delta$ or $J$ coupling leads to an incomplete rotation for components of the magnetization on the Bloch sphere, as highlighted in (b). Applying a strong orthogonal RF driving ($\Omega_2/2\pi = 200\,\mathrm{kHz}$) in the measure stage performs a $2\pi n_2$, pulse causing any components of the magnetization in the $x$-$z$ plane to oscillate with frequency $\Omega_2$ and amplitude $\propto \delta^2$, as in Eq.(\ref{['Eq: NSLsignal']}). Simultaneously, MW pulses are applied to couple the NV to the generated RF signal. This is repeated $R$ times, with NV measurements stored between repetitions. (c) A comparison of the sensitivity of continuous AERIS, $\eta$, to that of standard AERIS, $\eta^*$, using Eq.(\ref{['Eq: compSens']}) for different $\Omega_1$, comparing both $T_{1\rho}$ (purple) and $\tilde{T}_\mathrm{1\rho}$ (gray). For the Rabi frequency considered here, an enhancement in sensitivity by approximately a factor of 4 is expected. We take $n_1 = n_2 = 1$ and $R = 1000$. (d) The Fourier transform of simulations for the NMR signal gathered by an NV using continuous (blue) and standard AERIS (orange) for, from left to right, methyl acetate, trimethyl phosphate and chloroethane. The signal for chloroethane differs, with $\Omega_1/2\pi = 0.6\,\mathrm{kHz}$. The noise parameters have been taken to be the same as in Fig. \ref{['fig: driveShift']}. For continuous-AERIS, instead of plotting the frequency shift, $\omega$, on the $x$ axis, we map the spectrum to $\omega' = \sqrt{\omega^2 - \Omega_1^2}$ such that the spectral peaks align with standard AERIS. Both are plotted in dimensionless units (ppm).
• Figure S1: Comparisons of the $\tilde{T}_{1\rho}$ coherence time improvement in simulations with weak spin locking for a microscale NMR signal with different $T_2^*$ times and hence noise strengths $\sigma$. Note that this coherence time includes a $T_1$ decay as presented in Fig.2 in the main paper. We assume the same $T_1$ decay channel for all cases. Signals with noise strengths of $\sigma = 3,10,30\,\mathrm{Hz}$ are considered corresponding to coherence times $T_2^* \simeq 600,\,60,\,6\,\mathrm{ms}$ respectively for the same correlation time $\tau_c = 4.6\,\mathrm{ms}$. (a) The expected increase in the coherence time including a $T_1 = 1.5 \,\mathrm{s}$ decay time for different spin locking Rabi frequencies and noise strengths. (b) A plot of the expected increase in sensitivity from Eq.\ref{['Eq: sensFull']} for different Rabi strengths and hence coherence times. The same parameters are taken in the main text, but with each noise strength taking different $R = 2500,\,250,\,25$ for noise strengths $\sigma = 3,10,30\,\mathrm{Hz}$, respectively.
• Figure S2: Comparisons of sensitivities between continuous and standard AERIS for different overhead times $t_o$ - calculated using Eq.\ref{['Eq: sensFullOver']}. As the NMR signal for standard AERIS has a shorter decay time $T_2^*$, more repeated scans $M$ are used compared to continuous AERIS. The overhead time used here provides a penalty on resetting the NMR signal, and hence for larger values of $t_o$, the ratio of sensitivities $\eta^*/\eta$ increases. In this figure, a signal with $T_2^* \simeq 60\,\mathrm{ms}$ and hence noise $\sigma = 10\,\mathrm{Hz}$ is studied.