Heteronuclear decoupling under fast MAS by a rotor-synchronized Hahn-echo pulse train

A new heteronuclear decoupling mechanism under fast magic-angle spinning MAS is introduced. It is based on refocusing the coherences responsible for the dephase of low-gamma nuclei ((13)C, (15)N) transverse spin-polarization in the presence of strongly dipolar-coupled protons, and has the advantage that can be implemented by pulsed techniques, with all the benefits resulting from a reduced duty cycle compared with conventional decoupling by continuous rf irradiation. The decoupling efficiency of a simple rotor-synchronized Hahn-echo pulse train is analyzed both theoretically and experimentally. It was found that a substantial improvement in sensitivity and resolution can be achieved in compounds with small (1)H chemical shielding parameters even at moderate sample spinning, and some interesting applications are shown. It is also shown that much faster spinning frequencies, or alternative refocusing sequences, are needed for applications on rigid organic solids, i.e., in systems with larger (1)H chemical shifts.     

Heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance under ultra-high magic-angle spinning

We compare in this communication several heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance experiments under a magic-angle spinning frequency of 60 kHz. The decoupling radiofrequency field amplitudes considered are 190 and 10 kHz. No substantial difference was found among the sequences considered here in performance barring the difference in the optimisation protocol of the various schemes, an aspect that favours the use of swept-frequency two pulse phase modulation (SW(f)-TPPM).     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

Second order gradient ascent pulse engineering

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of spin ensembles and other quantum systems. These include more accurate gradients, convergence acceleration using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.     

Application of optimal control to CPMG refocusing pulse design

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.     

Improved heteronuclear dipolar decoupling sequences for liquid-crystal NMR

Recently we introduced a radiofrequency pulse scheme for heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance under magic-angle spinning [R.S. Thakur, N.D. Kurur, P.K. Madhu, Swept-frequency two-pulse phase modulation for heteronuclear dipolar decoupling in solid-state NMR, Chem. Phys. Lett. 426 (2006) 459-463]. Variants of this sequence, swept-frequency TPPM, employing frequency modulation of different types have been further tested to improve the efficiency of heteronuclear dipolar decoupling. Among these, certain sequences that were found to perform well at lower spinning speeds are demonstrated here on a liquid-crystal sample of MBBA for application in static samples. The new sequences are compared with the standard TPPM and SPINAL schemes and are shown to perform better than them. These modulated schemes perform well at low decoupler radiofrequency power levels and are easy to implement on standard spectrometers.     

The influence of the molecular system on the performance of heteronuclear decoupling in solid-state NMR

The intensity of the carbon signal in a CPMAS experiment has been measured for two CH and three CH(2) moieties in four test molecules under different phase-modulated proton decoupling conditions and as a function of the spinning rate. The proton decoupling schemes investigated were the golden standard TPPM and three of the GTn family. Aim of this analysis was to better describe experimentally the impact and limitations of phase-modulated decoupling. Sizeable differences in the response to decoupling were observed in otherwise chemically identical molecular fragments, such as the CHCH(2) found in tyrosine, phenyl-succinic acid or 9-Anthrylmethyl-malonate, probably due to differences in spin-diffusion rates. In keeping with known facts, the efficiency of the decoupling was observed to decrease with the MAS rate, but with somewhat different trends for the tested systems.     

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.     

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

A novel class of pulses is presented which can be regarded as a generalization of both frequency-selective pulses and B1-selective pulses. The excitation profile of these pulses forms a pre-defined pattern in two dimensions, which are spanned by pulse offset and radio-frequency (RF) amplitude. The presented pulses were designed numerically based on principles of optimal control theory. For simple test patterns, we demonstrate the flexibility of this approach by simulations and experiments. This previously unknown flexibility may trigger novel applications in NMR spectroscopy and imaging. As a first practical application, we demonstrate a direct approach for calibrating RF pulses.     

An analysis of phase-modulated heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance

The design of variants of the swept-frequency two-pulse phase modulation sequence for heteronuclear dipolar decoupling in solid-state NMR is reported, their performance evaluated, and compared with other established sequences like TPPM and SPINAL. Simulations performed to probe the role of the homonuclear (1)H-(1)H bath show that the robustness of the decoupling schemes improves with the size of the bath. In addition, these simulations reveal that the homonuclear (1)H-(1)H bath also leads to broad baselines at high MAS rates. Results from a study of the SPINAL decoupling scheme indicate that optimisation of the starting phase and phase increment improves its performance and efficiency at high MAS rates. Additionally, experiments performed on a liquid crystal display the role of the initial phase in SPINAL-64 and sequences in the SW(f)-TPPM family.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

In this work, we investigate the accuracy of controlling spin I=1, 3/2 and 5/2 spin systems by average Hamiltonian theory. By way of example, we consider a simple two-pulse echo sequence and compare this perturbation scheme to a numerical solution of the Von Neumann equation. For the different values of I, we examine this precision as a function of the quadrupolar coupling as well as various experimental parameters such as the pulse spacing and pulse width. Experiments and simulations on I=3/2 and I=5/2 spin systems are presented that highlight a spectral artifact introduced due to finite pulse widths as predicted by average Hamiltonian theory. The control of these spin systems by this perturbation scheme is considered by investigating a phase cycling scheme that suppresses these artifacts to zeroth-order of the Magnus expansion.     

Finite pulse width artifact suppression in spin-1 quadrupolar echo spectra by phase cycling

A phase cycling scheme for suppressing spectral artifacts introduced in quadrupolar echo spectroscopy of spin-1 nuclei due to finite pulse width effects is presented. The phase cycling scheme is developed using the formalism of average Hamiltonian theory and fictitious spin-1 operators. A simulation and experiment on deuterated polyethelene is performed highlighting the spectral artifact introduced by finite pulse widths and successful removal with the proposed phase cycling scheme.     

Reduction in optimal control theory

A geometric setting for the Pontryagin maximum principle in optimal control theory is provided. The equations for critical trajectories are given in terms of a symplectic equation. These equations are generalized to the framework of Lie algebroids, giving thus a way to study reduction by symmetry groups of the maximum principle.     

Design and application of robust rf pulses for toroid cavity NMR spectroscopy

We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B? field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 μs) pulses with acceptable performance compared to standard implementations. OP also discovered a new class of non-adiabatic pulse shapes with improved performance within the BIR-4 framework. However, none of the OP-BIR4 pulses are competitive with the more generally optimized UR pulses. The advantages of the new pulses are demonstrated in simulations and experiments. In particular, the DQF COSY result presented here represents the first implementation of 2D NMR spectroscopy using a toroid probe.     

Using optimal control theory to identify network structures that foster synchrony

Network structures are known to influence a population’s propensity to synchronize. Previous attempts to identify synchrony promoting structures have focused on homogeneous populations. We use optimal control theory to construct networks that allow heterogeneous populations to maintain high levels of synchrony, explore the relationship between population heterogeneity and the structure of the optimal networks, and identify salient optimal network features that may enhance synchrony. In particular, we identify a new parameter, the average strength of neighbors, that may foster synchrony and observe that repulsion, in addition to attraction, can foster synchrony.     

Effects of experimental imperfections on a spin counting experiment

Spin counting NMR is an experimental technique that allows a determination of the size and time evolution of networks of dipolar coupled nuclear spins. This work reports on an average Hamiltonian treatment of two spin counting sequences and compares the efficiency of the two cycles in the presence of flip errors, RF inhomogeneity, phase transients, phase errors, and offset interactions commonly present in NMR experiments. Simulations on small quantum systems performed using the two cycles reveal the effects of pulse imperfections on the resulting multiple quantum spectra, in qualitative agreement with the average Hamiltonian calculations. Experimental results on adamantane are presented, demonstrating differences in the two sequences in the presence of pulse errors.