Coherent isotropic averaging in zero‐field nuclear magnetic resonance. I. General theory and icosahedral sequences

Lower than low: Perspectives on zero- to ultralow-field nuclear magnetic resonance

The less-traveled low road in nuclear magnetic resonance is discussed, honoring the contributions of Prof. Bernhard Blümich, aspiring towards reaching 'a new low.' A history of the subject and its current status are briefly reviewed, followed by an effort to prophesy possible directions for future developments.

Experimental benchmarking of quantum control in zero-field nuclear magnetic resonance

Demonstration of coherent control and characterization of the control fidelity is important for the development of quantum architectures such as nuclear magnetic resonance (NMR). We introduce an experimental approach to realize universal quantum control, and benchmarking thereof, in zero-field NMR, an analog of conventional high-field NMR that features less-constrained spin dynamics. We design a composite pulse technique for both arbitrary one-spin rotations and a two-spin controlled-not (CNOT) gate in a heteronuclear two-spin system at zero field, which experimentally demonstrates universal quantum control in such a system. Moreover, using quantum information-inspired randomized benchmarking and partial quantum process tomography, we evaluate the quality of the control, achieving single-spin control for ¹³C with an average fidelity of 0.9960(2) and two-spin control via a CNOT gate with a fidelity of 0.9877(2). Our method can also be extended to more general multispin heteronuclear systems at zero field. The realization of universal quantum control in zero-field NMR is important for quantum state/coherence preparation, pulse sequence design, and is an essential step toward applications to materials science, chemical analysis, and fundamental physics.

13C-Decoupled J-Coupling Spectroscopy Using Two-Dimensional Nuclear Magnetic Resonance at Zero-Field

We present a two-dimensional method for obtaining ¹³C-decoupled, ¹H-coupled nuclear magnetic resonance (NMR) spectra in zero magnetic field using coherent spin-decoupling. The result is a spectrum determined only by the proton-proton J-coupling network. Detection of NMR signals in zero magnetic field requires at least two different nuclear spin species, but the proton J-spectrum is independent of isotopomer, thus potentially simplifying spectra and thereby improving the analytical capabilities of zero-field NMR. The protocol does not rely on a difference in Larmor frequency between the coupled nuclei, allowing for the direct determination of J-coupling constants between chemically equivalent spins. We obtain the ¹³C-decoupled zero-field spectrum of [1-¹³C]-propionic acid and identify conserved quantum numbers governing the appearance of cross peaks in the two-dimensional spectrum.

Optical detection of NMR J-spectra at zero magnetic field

Scalar couplings of the form JI(1) x I(2) between nuclei impart valuable information about molecular structure to nuclear magnetic-resonance spectra. Here we demonstrate direct detection of J-spectra due to both heteronuclear and homonuclear J-coupling in a zero-field environment where the Zeeman interaction is completely absent. We show that characteristic functional groups exhibit distinct spectra with straightforward interpretation for chemical identification. Detection is performed with a microfabricated optical atomic magnetometer, providing high sensitivity to samples of microliter volumes. We obtain 0.1 Hz linewidths and measure scalar-coupling parameters with 4-mHz statistical uncertainty. We anticipate that the technique described here will provide a new modality for high-precision "J spectroscopy" using small samples on microchip devices for multiplexed screening, assaying, and sample identification in chemistry and biomedicine.

High-resolution NMR of static samples by rotation of the magnetic field

Mechanical rotation of a sample at 54.7 degrees with respect to the static magnetic field, so-called magic-angle spinning (MAS), is currently a routine procedure in nuclear magnetic resonance (NMR). The technique enhances the spectral resolution by averaging away anisotropic spin interactions thereby producing isotropic-like spectra with resolved chemical shifts and scalar couplings. It should be possible to induce similar effects in a static sample if the direction of the magnetic field is varied, e.g., magic-angle rotation of the B0 field (B0-MAS). Here, this principle is experimentally demonstrated in a static sample of solid hyperpolarized xenon at approximately 3.4 mT. By extension to moderately high fields, it is possible to foresee interesting applications in situations where physical manipulation of the sample is inconvenient or impossible. Such situations are expected to arise in many cases from materials to biomedicine and are particularly relevant to the novel approach of ex situ NMR spectroscopy and imaging.

Computation of Orientational Averages in Solid-State NMR by Gaussian Spherical Quadrature

We investigate Gaussian spherical quadrature as a method for calculating orientational averages in solid-state NMR. For the case of magic-angle-spinning sideband amplitudes of isolated spins-1/2, we demonstrate the superiority of Gaussian spherical quadrature over other orientational averaging methods. Depending on the shift anisotropy parameters and the desired accuracy, the computation speed is enhanced by a large factor (between two and many hundreds). In addition, a method for improving any present sampling scheme is devised. Such schemes are called SHREWD (Spherical Harmonic Reduction or Elimination by a Weighted Distribution). The role of orientational symmetry in solid-state NMR is explored. We also discuss the limitations of the Gaussian spherical quadrature methods. Copyright 1998 Academic Press.

Effects of the finite pulse widths on solid echo signals

The quadrupolar and dipolar interactions of spins during the radio frequency (RF) pulses are considered. It is shown that due to these interactions the two-pulse echo signal is observed at the shifted time t(e) = tau + t1/2 (t1 = width of the first RF pulse, tau = time interval between the pulses).

NQR transient nutation and rotary echoes in the effective field of multiple-pulse sequences

We present the results of the experimental investigations of the transient processes preceding the establishment of quasistationary states in multiple-pulse nuclear quadrupole resonance. It is shown that the inversion of the phase of radio frequency pulses in the pulse sequence or an extra pulse produces the echo signal in the effective field of the multiple-pulse sequence (the echo on the envelope of echo signals). The train of the echo signals in the effective field is also obtained. The application of this technique for the investigation of the dipole-dipole interactions in spin systems with large inhomogeneous broadening is discussed.