Dual-compensated antisymmetric composite refocusing pulses for NMR

Towards shorter composite 180° refocusing pulses for NMR

Novel composite 180° pulses are designed for use in nuclear magnetic resonance (NMR) and verified experimentally using solution-state 1H NMR spectroscopy. Rather than being constructed from 180° pulses (as in much recent work), the new composite pulses are constructed from 90° pulses, with the aim of finding sequences that are shorter overall than existing equivalents. The primary (but not exclusive) focus is on composite pulses that are dual compensated - simultaneously broadband with respect to both inhomogeneity of the radiofrequency field and resonance offset - and have antisymmetric phase schemes, such that they can be used to form spin echoes without the introduction of a phase error. In particular, a new antisymmetric dual-compensated refocusing pulse is presented that is constructed from ten 90° pulses, equivalent to just five 180° pulses.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Three-state coherent control using narrowband and passband sequences

In this work, we propose a comprehensive design for narrowband and passband composite pulse sequences by involving the dynamics of all states in the three-state system. The design is quite universal as all pulse parameters can be freely employed to modify the coefficients of error terms. Two modulation techniques, the strength and phase modulations, are used to achieve arbitrary population transfer with a desired excitation profile, while the system keeps minimal leakage to the third state. Furthermore, the current sequences are capable of tolerating inaccurate waveforms, detuning errors, and work well when rotating wave approximation is not strictly justified. Therefore, this work provides versatile adaptability for shaping various excitation profiles in both narrowband and passband sequences.

Composite pulse combinations for chirp excitation

Composite pulses are the efficient method for broadband excitation to get control of the limitations of high field NMR, such as resonance offset effects with constraints on rf power that leads to signal intensity distortion. Phase-modulated chirp pulses are used as ordered composite pulse sequences in this paper as CHORUS sequence in a high-field NMR spectrometer (BRUKER 750 MHz) for broadband excitation. The composite pulse sequence applies chirp pulses with the forward and the reverse sweep mechanisms. A single excitation pulse combines adiabatic and non-adiabatic rotation, explained as a three-phase rotation, which leaves the magnetizing vectors to a non-uniform phase dispersion as a function of the offset frequency. One adiabatic refocusing pulse of the double sweep rate after the excitation pulse cannot satisfactorily compensate for the phase dispersion. Hence, composite self-refocussing CHORUS excitation pulse, with forward, reverse, and their combinations are used to remove the non-uniform phase dispersion generated due to offset resonance frequency. Four such combinations of composite pulses are produced with analytical explanation in this paper. MATLAB simulation results and experimental verification on the BRUKER 750 MHz NMR spectrometer of the composite pulses are also presented in this paper.

Improved sensitivity and quantification for 29Si NMR experiments on solids using UDEFT (Uniform Driven Equilibrium Fourier Transform)

We demonstrate the possibility to use UDEFT (Uniform Driven Equilibrium Fourier Transform) technique in order to improve the sensitivity and the quantification of one-dimensional ²⁹Si NMR experiments under magic-angle spinning (MAS). We derive an analytical expression of the signal-to-noise ratios of UDEFT and single-pulse (SP) experiments subsuming the contributions of transient and steady-state regimes. Using numerical spin dynamics simulations and experiments on ²⁹Si-enriched amorphous silica and borosilicate glass, we show that 59₁₈₀298₀59₁₈₀ refocusing composite π-pulse and the adiabatic inversion using tanh/tan modulation improve the robustness of UDEFT technique to rf-inhomogeneity, offset, and chemical shift anisotropy. These pulses combined with a two-step phase cycle limit the pulse imperfections and the artifacts produced by stimulated echoes. The sensitivity of SP, UDEFT and CPMG (Carr-Purcell-Meiboom-Gill) techniques are experimentally compared on functionalized and non-functionalized mesoporous silica. Furthermore, experiments on a flame retardant material prove that UDEFT technique provides a better quantification of ²⁹Si sites with higher sensitivity than SP method.

Enhancing the sensitivity of multidimensional NMR experiments by using triply-compensated π pulses

In multidimensional solution NMR experiments, π pulses are used extensively for inversion and refocusing operations on 1H, 13C and 15N nuclei. Pulse miscalibration, off-resonance effects, and J-coupling evolution during π pulse execution result in severe signal losses that are exacerbated at high magnetic fields. Here, we report the implementation of a triply-compensated π pulse (G5) optimized for both inversion and refocusing in widely used 2- and 3-dimensional experiments. By replacing most of the hard π pulses, adiabatic or composite pulses on the 1H, 13C and 15N channels with G5 pulses, we obtained signal enhancements ranging from 80 to 240%. We anticipate that triply-compensated pulses will be crucial for improving the performance of multidimensional and multinuclear pulse sequences at ultra-high fields.

Very broadband diffusion-ordered NMR spectroscopy: (19)F DOSY

A new pulse sequence, CHORUS Oneshot, allows measurements of diffusion-ordered spectroscopy (DOSY) spectra over the full chemical shift range of (19)F for the first time. Swept-frequency pulses are used to give very broadband excitation; the sequence is a prototype for a large family of very broadband liquid state NMR methods.

Increasing the quantitative bandwidth of NMR measurements

The frequency range of quantitative NMR is increased to hundreds of kHz, yielding accurate integrals even for ¹⁹F.

Genetic algorithm optimized triply compensated pulses in NMR spectroscopy

Sensitivity and resolution in NMR experiments are affected by magnetic field inhomogeneities (of both external and RF), errors in pulse calibration, and offset effects due to finite length of RF pulses. To remedy these problems, built-in compensation mechanisms for these experimental imperfections are often necessary. Here, we propose a new family of phase-modulated constant-amplitude broadband pulses with high compensation for RF inhomogeneity and heteronuclear coupling evolution. These pulses were optimized using a genetic algorithm (GA), which consists in a global optimization method inspired by Nature's evolutionary processes. The newly designed π and π/2 pulses belong to the 'type A' (or general rotors) symmetric composite pulses. These GA-optimized pulses are relatively short compared to other general rotors and can be used for excitation and inversion, as well as refocusing pulses in spin-echo experiments. The performance of the GA-optimized pulses was assessed in Magic Angle Spinning (MAS) solid-state NMR experiments using a crystalline U-(13)C, (15)N NAVL peptide as well as U-(13)C, (15)N microcrystalline ubiquitin. GA optimization of NMR pulse sequences opens a window for improving current experiments and designing new robust pulse sequences.

Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors

Composite pulses have found widespread use in both conventional Nuclear Magnetic Resonance experiments and in experimental quantum information processing to reduce the effects of systematic errors. Here we describe several families of time symmetric and antisymmetric fully compensating composite pulses, inspired by the previous Fn, Gn and BB1 families family developed by Wimperis. We describe families of composite 180° pulses (not gates) which exhibit unprecedented tolerance of pulse strength errors without unreasonable sensitivity to off-resonance errors, and related families with more exotic tailored responses. Next we address the problem of extending these methods to other rotation angles, and discuss numerical results for 90° pulses. Finally we demonstrate the performance of some 90° and 180° pulses in NMR experiments.