Blueprint for nanoscale NMR

Ilai Schwartz,Fedor Jelezko,Benedikt Tratzmiller,Joachim Rosskopf,Liam P Mcguinness,Qiong Chen,Martin B Plenio,Simon Schmitt

doi:10.1038/s41598-019-43404-2

Abstract

Nitrogen vacancy (NV) centers in diamond have been used as ultrasensitive magnetometers to perform nuclear magnetic resonance (NMR) spectroscopy of statistically polarized samples at 1–100 nm length scales. However, the spectral linewidth is typically limited to the kHz level, both by the NV sensor coherence time and by rapid molecular diffusion of the nuclei through the detection volume which in turn is critical for achieving long nuclear coherence times. Here we provide a blueprint supported by detailed theoretical analysis for a set-up that combines a sensitivity sufficient for detecting NMR signals from nano- to micron-scale samples with a spectral resolution that is limited only by the nuclear spin coherence, i.e. comparable to conventional NMR. Our protocol detects the nuclear polarization induced along the direction of an external magnetic field with near surface NV centers using lock-in detection techniques to enable phase coherent signal averaging. Using the NV centers in a dual role of NMR detector and optical hyperpolarization source to increase signal to noise, and in combination with Bayesian inference models for signal processing, nano/microscale NMR spectroscopy can be performed on sample concentrations in the micromolar range, several orders of magnitude better than the current state of the art.

Highlights

MethodsAll simulations were performed using a 6.1 nm or 12.2 nm deep Nitrogen vacancy (NV) center, with the diffusion coefficient of 10−12 m2/s
For bulk samples, the thermal polarization greatly exceeds the statistical polarization fluctuations. This allows on the one hand for the controlled initialization of the signal and phase coherent signal accumulation resulting in a rapid growth of the signal to noise ratio (SNR) and on the other hand for long signal coherence times and high spectral resolution
We use three key features to compensate for this apparent shortcoming, namely, (i) the signal phase can be controlled by an initializing π/2-pulse to allow for phase coherent accumulation across subsequent measurements, (ii) because the thermal polarization component is uniform across the entire sample beyond the immediate detection region, the signal coherence time becomes essentially independent of diffusion allowing for high spectral resolution, (iii) and for the same reasons the signal is uniform across the sample which allows for the use of multiple Nitrogen vacancy (NV)-centers for simultaneous signal acquisition further improving SNR

Summary

Methods

All simulations were performed using a 6.1 nm or 12.2 nm deep NV center, with the diffusion coefficient of 10−12 m2/s. For the simulation of the toluene molecule, a 12.2 nm deep NV was used with 0.2 M concentration at 0.25 T magnetic field, using XY8-8 sensing sequences for the signal accumulations and a delay time of 64 ns between the pulses. In Bayesian statistics, a model of those aspects of the experiment that are relevant to the detected signal is built, and within this model parameters are considered as random variables. An estimation problem is equivalent to the determination of the distribution of those parameters. For brevity of the manuscript, the model, parameters and algorithms are presented in detail in the Supplementary Information

Results

Discussion

Conclusion