Continuous Floquet theory in solid-state NMR.

This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.

Interaction frames in solid-state NMR: A case study for chemical-shift-selective irradiation schemes.

Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual (Zeeman) rotating frame, or the radio-frequency-field (rf) Hamiltonian to describe the efficiency of decoupling or recoupling sequences. Going into an interaction frame can also make parts of a time-dependent Hamiltonian time independent like the rf-field Hamiltonian in the usual (Zeeman) rotating frame. Eliminating the dominant term often allows a better understanding of the details of the spin dynamics. Going into an interaction frame can also reduces the energy-level splitting in the Hamiltonian leading to a faster convergence of perturbation expansions, average Hamiltonian, or Floquet theory. Often, there is no obvious choice of the interaction frame to use but some can be more convenient than others. Using the example of frequency-selective dipolar recoupling, we discuss the differences, advantages, and disadvantages of different choices of interaction frames. They always include the complete radio-frequency Hamiltonian but can also contain the chemical shifts of the spins and may or may not contain the effective fields over one cycle of the pulse sequence.

A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR.

We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.

Biomolecular solid-state NMR spectroscopy at 1200 MHz: the gain in resolution.

Progress in NMR in general and in biomolecular applications in particular is driven by increasing magnetic-field strengths leading to improved resolution and sensitivity of the NMR spectra. Recently, persistent superconducting magnets at a magnetic field strength (magnetic induction) of 28.2 T corresponding to 1200 MHz proton resonance frequency became commercially available. We present here a collection of high-field NMR spectra of a variety of proteins, including molecular machines, membrane proteins, viral capsids, fibrils and large molecular assemblies. We show this large panel in order to provide an overview over a range of representative systems under study, rather than a single best performing model system. We discuss both carbon-13 and proton-detected experiments, and show that in 13C spectra substantially higher numbers of peaks can be resolved compared to 850 MHz while for 1H spectra the most impressive increase in resolution is observed for aliphatic side-chain resonances.

Residual dipolar line width in magic-angle spinning proton solid-state NMR.

Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1/ωr dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ωr-2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

Generation of single photons with highly tunable wave shape from a cold atomic ensemble.

The generation of ultra-narrowband, pure and storable single photons with widely tunable wave shape is an enabling step toward hybrid quantum networks requiring interconnection of remote disparate quantum systems. It allows interaction of quantum light with several material systems, including photonic quantum memories, single trapped ions and opto-mechanical systems. Previous approaches have offered a limited tuning range of the photon duration of at most one order of magnitude. Here we report on a heralded single photon source with controllable emission time based on a cold atomic ensemble, which can generate photons with temporal durations varying over three orders of magnitude up to 10 µs without a significant change of the readout efficiency. We prove the nonclassicality of the emitted photons, show that they are emitted in a pure state, and demonstrate that ultra-long photons with nonstandard wave shape can be generated, which are ideally suited for several quantum information tasks.

APOA5 Q97X mutation identified through homozygosity mapping causes severe hypertriglyceridemia in a Chilean consanguineous family.

BACKGROUND: Severe hypertriglyceridemia (HTG) has been linked to defects in LPL, APOC2, APOA5, LMF1 and GBIHBP1 genes. However, a number of severe HTG cases are probably caused by as yet unidentified mutations. Very high triglyceride plasma levels (>112 mmol/L at diagnosis) were found in two sisters of a Chilean consanguineous family, which is strongly suggestive of a recessive highly penetrant mutation. The aim of this study was to determine the genetic locus responsible for the severe HTG in this family. METHODS: We carried out a genome-wide linkage study with nearly 300,000 biallelic markers (Illumina Human CytoSNP-12 panel). Using the homozygosity mapping strategy, we searched for chromosome regions with excess of homozygous genotypes in the affected cases compared to non-affected relatives. RESULTS: A large homozygous segment was found in the long arm of chromosome 11, with more than 2,500 consecutive homozygous SNP shared by the proband with her affected sister, and containing the APOA5/A4/C3/A1 cluster. Direct sequencing of the APOA5 gene revealed a known homozygous nonsense Q97X mutation (p.Gln97Ter) found in both affected sisters but not in non-affected relatives nor in a sample of unrelated controls. CONCLUSION: The Q97X mutation of the APOA5 gene in homozygous status is responsible for the severe hypertriglyceridemia in this family. We have shown that homozygosity mapping correctly pinpointed the genomic region containing the gene responsible for severe hypertriglyceridemia in this consanguineous Chilean family.