R. Tycko

Composite pulses without phase distortion

Abstract Composite pulses for broadband spin excitation over large ranges of radiofrequency field amplitudes and resonance offsets are presented. They are derived according to a previously presented method based on the Magnus expansion in the manner of coherent averaging theory. It is shown theoretically and in simulations that these composite pulses do not introduce a strong dependence of the NMR signal phase on the rf amplitude or resonance offset, overcoming a common problem of composite pulses derived by other means. Experimental demonstrations include the use of composite π pulses for refocusing transverse magnetization in spin-echo sequences and the use of composite π 2 pulses in a simple multiple-pulse experiment. Further applications are discussed.

Fixed point theory of iterative excitation schemes in NMR

Iterative schemes for NMR have been developed by several groups. A theoretical framework based on mathematical dynamics is described for such iterative schemes in nonlinear NMR excitation. This is applicable to any system subjected to coherent radiation or other experimentally controllable external forces. The effect of the excitation, usually a pulse sequence, can be summarized by a propagator or superpropagator (U). The iterative scheme (F) is regarded as a map of propagator space into itself, U n+1=F U n . One designs maps for which a particular propagator U or set of propagators {U} is a fixed point or invariant set. The stability of the fixed points along various directions is characterized by linearizing F around the fixed point, in analogy to the evaluation of an average Hamiltonian. Stable directions of fixed points typically give rise to broadband behavior (in parameters such as frequency, rf amplitude, or coupling constants) and unstable directions to narrowband behavior. The dynamics of the maps are illustrated by ‘‘basin images’’ which depict the convergence of points in propagator space to the stable fixed points. The basin images facilitate the optimal selection of initial pulse sequences to ensure convergence to a desired excitation. Extensions to iterative schemes with several fixed points are discussed. Maps are shown for the propagator space S O(3) appropriate to iterative schemes for isolated spins or two‐level systems. Some maps exhibit smooth, continuous dynamics whereas others have basin images with complex and fractal structures. The theory is applied to iterative schemes for broadband and narrowband π (population inversion) and π/2 rotations, MLEV and Waugh spin decoupling sequences, selective n‐quantum pumping, and bistable excitation.

Broadband population inversion by phase modulated pulses

We present a class of continuously phase modulated radiation pulses that result in coherent population inversion over a large range of transition frequencies. The continuously modulated pulses can be approximated by sequences of discrete phase shifted pulses. Simulations of the inversion properties of the continuously modulated pulses and of the discrete pulse sequences are given.

Iterative schemes for broad-band and narrow-band population inversion in NMR

Abstract We derive iterative schemes for generating rf pulse sequences that invert nuclear spin populations over either broad or narrow ranges of resonance offsets and rf amplitudes. The schemes employ only phase shifting and concatenation operations. Iterative application of a scheme produces a series of pulse sequences with successive improvements in population inversion performance.

Broadband population inversion in solid state NMR

We present theory, simulations and experimental demonstrations of composite π pulses for population inversion in coupled spin systems such as occur in solid state NMR. The composite π pulses are phase‐shifted rf pulse sequences designed to invert spins over a larger range of dipole or quadrupole couplings than a conventional π pulse, for a given rf power. We discuss a previously proposed theory for constructing composite pulses, in the specific context of solids. Two particular sequences 450180909018018090450 and 18001801201800 are examined in detail. Their performance in coupled spin systems of various sizes is evaluated in simulations. Experiments are performed on two solid compounds, Ba(ClO3)2⋅H2O and C4O4H2. The results reveal markedly less spectral distortion after composite pulse inversion than after conventional π pulse inversion at low rf powers.

Composite sequences for efficient double-quantum Excitation over a range of spin coupling strengths

Abstract It is demonstrated theoretically and experimentally that double-quantum coherence can be excited with nearly maximal efficiency over a large range of spin coupling strengths in NMR with the use of composite excitation sequences. Such sequences are shown to be directly constructible from existing composite π 2 pulses. In addition, a general procedure is given for converting a composite excitation sequence to an equivalent, reduced form that contains fewer rf pulses and simpler rf phase shifts. Experiments are performed on the proton pair of CH2Cl2 oriented in a liquid crystal solvent. Applications to quadrupolar spin-1 nuclei and other dynamically simple multilevel systems are discussed.

Spin diffusion between inequivalent quadrupolar nuclei by double-quantum flip-flops

Abstract A new mechanism for spin diffusion between quadrupolar nuclei whose NMR lines do not overlap is proposed. For spin-1 nuclei, double-quantum flip-flop transitions allow the diffusion of Zeeman order, but not quadrupolar order, without requiring an extraneous energy reservoir. The flip-flop rate is sensitive to the relative signs of the quadrupolar splittings.

Spatially selective NMR with broad-band radiofrequency pulses

Abstract The problem of non-invasive spatial localization in NMR is approached by constructing a spatially selective composite pulse sequence and incorporating it into a recently developed difference scheme. The composite sequence described, which requires nine phase-shifted π pulses, functions only over a narrow range of radio-frequency (rf) field strengths while remaining effective over a broad range of resonance frequencies. Relying upon the field gradient of a surface coil to label regions in space by local rf amplitudes, the pulse inverts all nuclear spins at a selected distance from the coil across a broad range of chemical shifts. This approach will allow the observation of chemically shifted NMR signals from specific regions of a material or organism. Computer simulations are presented, and the method is demonstrated experimentally on a phantom sample using a surface coil.

Time-resolved optical nuclear polarization by rapid field switching

Abstract A novel time-resolved ONP technique is presented using pulsed UV excitation and rapid magnetic field switching. The potential of the new technique for studying excited triplet state dynamics on the microsecond time scale is demonstrated on a fluorene/acridine crystal. The technique also yields a significant enhancement of the ONP effect compared to constant-field experiments.