Spin-Noise-Detected Two-Dimensional Fourier-Transform NMR Spectroscopy

Correlated Spectroscopy of Electric Noise with Color Center Clusters

Experimental noise often contains information about the interactions of a system with its environment, but establishing a relation between the measured time fluctuations and the underlying physical observables is rarely apparent. Here, we leverage a multidimensional and multisensor analysis of spectral diffusion to investigate the dynamics of trapped carriers near subdiffraction clusters of nitrogen-vacancy (NV) centers in diamond. We establish statistical correlations in the spectral fluctuations we measure as we recursively probe the cluster optical resonances, which we then exploit to reveal proximal traps. Further, we deterministically induce Stark shifts in the cluster spectrum, ultimately allowing us to pinpoint the relative three-dimensional positions of interacting NVs as well as the location and charge sign of surrounding traps. Our results can be generalized to other color centers and provide opportunities for the characterization of photocarrier dynamics in semiconductors and the manipulation of nanoscale spin-qubit clusters connected via electric fields.

Spin noise gradient echoes

Nuclear spin noise spectroscopy in the absence of radio frequency pulses was studied under the influence of pulsed field gradients (PFGs) on pure and mixed liquids. Under conditions where the radiation-damping-induced line broadening is smaller than the gradient-dependent inhomogeneous broadening, echo responses can be observed in difference spectra between experiments employing pulsed field gradient pairs of the same and opposite signs. These observed spin noise gradient echoes (SNGEs) were analyzed through a simple model to describe the effects of transient phenomena. Experiments performed on high-resolution nuclear magnetic resonance (NMR) probes demonstrate how refocused spin noise behaves and how it can be exploited to determine sample properties. In bulk liquids and their mixtures, transverse relaxation times and translational diffusion constants can be determined from SNGE spectra recorded following tailored sequences of magnetic field gradient pulses.

A General Reconstruction Method for Multidimensional Sparse Sampling Nuclear Magnetic Resonance Spectroscopy

Multidimensional NMR spectroscopy provides a powerful tool for structure elucidation and dynamic analysis of complex samples, particularly for biological macromolecules. Multidimensional sparse sampling effectively accelerates NMR experiments while an efficient reconstruction method is generally required for unraveling spectra. Various reconstruction methods were proposed for pure Fourier NMR (only involving chemical shifts and J couplings detection). However, reconstruction concerned with Laplace-related NMR (i.e., involving relaxation or diffusion detection) is more challenging due to its ill-posed property. The existing Laplace-related NMR sparse sampling reconstruction methods suffer from poor resolution and possible artifacts in the resulting spectra owing to the pitfalls of the optimization algorithms. Herein, we propose a general approach for fast high-resolution reconstruction of multidimensional sparse sampling NMR, including pure Fourier, mixed Fourier-Laplace, and pure Laplace NMR, benefiting from the comprehensive sparse constraint and effective optimization algorithm and thus showing the promising prospects of multidimensional NMR.

NMR-based metabolomics with enhanced sensitivity

NMR-based metabolomics, which emerged along with mass spectrometry techniques, is the preferred method for studying metabolites in medical research and food industries. However, NMR techniques suffer from inherently low sensitivity, regardless of their superior reproducibility. To overcome this, we made two beneficial modifications: we detuned the probe to reach a position called "Spin Noise Tuning Optimum" (SNTO), and we replaced the conventional cylindrical 5 mm NMR tube with an electric field component-optimized shaped tube. We found that concerted use of both modifications can increase the sensitivity (signal to noise ratio per unit volume) and detection of metabolites and decrease the measurement time by order of magnitude. In this study, we demonstrate and discuss the achieved signal enhancement of metabolites on model non-human (bovine serum, amino acid standard mixture) and human urine samples.

Nuclear spin noise tomography in three dimensions with iterative simultaneous algebraic reconstruction technique (SART) processing

We report three-dimensional spin noise imaging (SNI) of nuclear spin density from spin noise data acquired by Faraday detection. Our approach substantially extends and improves the two-dimensional SNI method for excitation-less magnetic resonance tomography reported earlier (Müller and Jerschow, 2006). This proof of principle was achieved by taking advantage of the particular continuous nature of spin noise acquired in the presence of constant magnitude magnetic field gradients and recent advances in nuclear spin noise spectroscopy acquisition as well as novel processing techniques. In this type of projection-reconstruction-based spin noise imaging the trade-off between signal-to-noise ratio (or image contrast) and resolution can be adjusted a posteriori during processing of the original time-domain data by iterative image reconstruction in a unique way not possible in conventional rf-pulse-dependent magnetic resonance imaging (MRI). The 3D SNI is demonstrated as a proof of concept on a commercial 700 MHz high-resolution NMR spectrometer, using a 3D-printed polymeric phantom immersed in water.

Enhancement of the Nuclear Spin Noise Signal Using Wavelet Transform

Spin noise spectroscopy has attracted considerable attention recently owing partly to intrinsic interest in the phenomenon and partly to its significant application potential. Here, we address the inherent problem of low sensitivity of nuclear spin noise and examine the utility of wavelet transform to mitigate this problem by distinguishing real peaks from the noise contaminated data. Suppression of the random circuit noise and the consequent enhancement of the correlated nuclear spin noise signal have been demonstrated with discrete wavelet transform. Spectra of both ¹ H and ¹³ C nuclear spins have been considered and significant signal enhancements in both the cases have been observed. A detailed analysis of several possible wavelet, thresholding and decomposition solutions have been made to obtain the optimum condition for signal enhancement. It is observed that the application of wavelet transform leaves the spin noise signal line shape essentially unchanged, which is an advantage for several applications involving spin noise spectra.

Spin-Noise-Detected Two-Dimensional Nuclear Magnetic Resonance at Triple Sensitivity

A major breakthrough in speed and sensitivity of 2 D spin-noise-detected NMR is achieved owing to a new acquisition and processing scheme called "double block usage" (DBU) that utilizes each recorded noise block in two independent cross-correlations. The mixing, evolution, and acquisition periods are repeated head-to-tail without any recovery delays and well-known building blocks of multidimensional NMR (constant-time evolution and quadrature detection in the indirect dimension as well as pulsed field gradients) provide further enhancement and artifact suppression. Modified timing of the receiver electronics eliminates spurious random excitation. We achieve a threefold sensitivity increase over the original snHMQC (spin-noise-detected heteronuclear multiple quantum correlation) experiment (K. Chandra et al., J. Phys. Chem. Lett. 2013, 4, 3853) and demonstrate the feasibility of spin-noise-detected long-range correlation.

Nonlinear detection of secondary isotopic chemical shifts in NMR through spin noise

The detection of minor species in the presence of large amounts of similar main components remains a key challenge in analytical chemistry, for instance, to obtain isotopic fingerprints. As an alternative to the classical NMR scheme based on coherent excitation and detection, here we introduce an approach based on spin-noise detection. Chemical shifts and transverse relaxation rates are determined using only the detection circuit. Thanks to a nonlinear effect in mixtures with small chemical shift dispersion, small signals on top of a larger one can be observed with increased sensitivity as bumps on a dip; the latter being the signature of the main magnetization. Experimental observations are underpinned by an analytical theory: the coupling between the magnetization and the coil provides an amplified detection capability of both small static magnetic field inhomogeneities and small NMR signals. This is illustrated by two-bond ¹²C/¹³C isotopic measurements.

Nuclear spin noise allows passive monitoring of magnetization using the sole NMR detection circuit. Here, the authors report spectroscopic signatures of low abundance molecules and of weak magnetic field gradients which are nonlinearly amplified by cooled-coil probes and large overlapping signals.

Use of Nuclear Spin Noise Spectroscopy to Monitor Slow Magnetization Buildup at Millikelvin Temperatures

At ultralow temperatures, longitudinal nuclear magnetic relaxation times become exceedingly long and spectral lines are very broad. These facts pose particular challenges for the measurement of NMR spectra and spin relaxation phenomena. Nuclear spin noise spectroscopy is used to monitor proton spin polarization buildup to thermal equilibrium of a mixture of glycerol, water, and copper oxide nanoparticles at 17.5 mK in a static magnetic field of 2.5 T. Relaxation times determined in such a way are essentially free from perturbations caused by excitation radiofrequency pulses, radiation damping, and insufficient excitation bandwidth. The experimental spin-lattice relaxation times determined on resonance by saturation recovery with spin noise detection are consistently longer than those determined by using pulse excitation. These longer values are in better accordance with the expected field dependence trend than those obtained by on-resonance experiments with pulsed excitation.

The theory of spin noise spectroscopy: a review

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.

Nuclear spin noise in NMR revisited

The theoretical shapes of nuclear spin-noise spectra in NMR are derived by considering a receiver circuit with finite preamplifier input impedance and a transmission line between the preamplifier and the probe. Using this model, it becomes possible to reproduce all observed experimental features: variation of the NMR resonance linewidth as a function of the transmission line phase, nuclear spin-noise signals appearing as a "bump" or as a "dip" superimposed on the average electronic noise level even for a spin system and probe at the same temperature, pure in-phase Lorentzian spin-noise signals exhibiting non-vanishing frequency shifts. Extensive comparisons to experimental measurements validate the model predictions, and define the conditions for obtaining pure in-phase Lorentzian-shape nuclear spin noise with a vanishing frequency shift, in other words, the conditions for simultaneously obtaining the spin-noise and frequency-shift tuning optima.

Dynamical theory of spin noise and relaxation: Prospects for real-time NMR measurements

Recent developments in theoretical aspects of spin noise and relaxation and their interrelationship reveal a modified spin density, distinct from the density matrix, as the necessary object to describe fluctuations in spin systems. These fluctuations are to be viewed as an intrinsic quantum mechanical property of such systems immersed in random magnetic environments and are observed as "spin noise" in the absence of any radio frequency excitation. With the prospect of ultrafast digitization, the role of spin noise in real-time parameter extraction for (NMR) spin systems, and the advantage over standard techniques, is of essential importance, especially for systems containing a small number of spins. In this article we outline prospects for harnessing the recent dynamical theory in terms of spin-noise measurement, with attention to real-time properties.

On the tuning of high-resolution NMR probes

Three optimum conditions for the tuning of NMR probes are compared: the conventional tuning optimum, which is based on radio-frequency pulse efficiency, the spin noise tuning optimum based on the line shape of the spin noise signal, and the newly introduced frequency shift tuning optimum, which minimizes the frequency pushing effect on strong signals. The latter results if the radiation damping feedback field is not in perfect quadrature to the precessing magnetization. According to the conventional RLC (resistor-inductor-capacitor) resonant circuit model, the optima should be identical, but significant deviations are found experimentally at low temperatures, in particular on cryogenically cooled probes. The existence of different optima with respect to frequency pushing and spin noise line shape has important consequences on the nonlinearity of spin dynamics at high polarization levels and the implementation of experiments on cold probes.

Spin noise spectroscopy beyond thermal equilibrium and linear response

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Dependence of NMR noise line shapes on tuning, matching, and transmission line properties

The tuning and matching conditions of rf circuits, as well as the properties of the transmission lines connecting these to the preamplifier, have direct consequences for NMR probe sensitivity and as for the optimum delivery of rf power to the sample. In addition, tuning/matching conditions influence radiation damping effects, which manifest themselves as fast signal flip-back and line broadening effects, and can lead to concentration-dependent frequency shifts. Previous studies have also shown that the appearance of spin-noise and absorbed circuit noise signals heavily depended on tuning settings. Consequently, all these phenomena are linked together. The mutual connections and interdependences of these effects are highlighted and reviewed here.