Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps.

Many of the ubiquitous experiments of biomolecular NMR, including [Formula: see text], [Formula: see text], and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including [Formula: see text] relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.

Accelerating 2D NMR relaxation dispersion experiments using iterated maps.

NMR relaxation dispersion experiments play a central role in exploring molecular motion over an important range of timescales, and are an example of a broader class of multidimensional NMR experiments that probe important biomolecules. However, resolving the spectral features of these experiments using the Fourier transform requires sampling the full Nyquist grid of data, making these experiments very costly in time. Practitioners often reduce the experiment time by omitting 1D experiments in the indirectly observed dimensions, and reconstructing the spectra using one of a variety of post-processing algorithms. In prior work, we described a fast, Fourier-based reconstruction method using iterated maps according to the Difference Map algorithm of Veit Elser (DiffMap). Here we describe coDiffMap, a new reconstruction method that is based on DiffMap, but which exploits the strong correlations between 2D data slices in a pseudo-3D experiment. We apply coDiffMap to reconstruct dispersion curves from an [Formula: see text] relaxation dispersion experiment, and demonstrate that the method provides fast reconstructions and accurate relaxation curves down to very low numbers of sparsely-sampled data points.

Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System.

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.