Coherent Averaging Effects in Magnetic Resonance

Haeberlen, Ulrich; Waugh, J. S.

doi:10.1103/physrev.175.453

Cited by 1,056 publications

(778 citation statements)

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“…Many periodic RF pulse sequences are designed using average Hamiltonian theory (AHT) 9 , where the necessary RF pulse sequence that generates a desired average Hamiltonian H avg over a time τ c must be determined (τ c is the length of the pulse sequence). Repeated application of the pulse sequence introduces frequencies into the dynamics that are integer multiples of 1 τc , which may result in higher-order contributions to H avg that degrade the sequence's performance.…”

Section: Introductionmentioning

confidence: 99%

Pseudorandom selective excitation in NMR

Walls

Coomes

2011

Journal of Magnetic Resonance

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In this work, average Hamiltonian theory is used to study selective excitation in a spin-1/2 system evolving under a series of small flip-angle θ−pulses (θ 1) that are applied either periodically [which corresponds to the DANTE pulse sequence] or aperiodically. First, an average Hamiltonian description of the DANTE pulse sequence is developed; such a description is determined to be valid either at or very far from the DANTE resonance frequencies, which are simply integer multiples of the inverse of the interpulse delay. For aperiodic excitation schemes where the interpulse delays are chosen pseudorandomly, a single resonance can be selectively excited if the θ-pulses' phases are modulated in concert with the time delays.Such a selective pulse is termed a pseudorandom-DANTE or p-DANTE sequence, and the conditions in which an average Hamiltonian description of p-DANTE is found to be similar to that found for the DANTE sequence. It is also shown that averaging over different p-DANTE sequences that are selective for the same resonance can help reduce excitations at frequencies away from the resonance frequency, thereby improving the apparent selectivity of the p-DANTE sequences. Finally, experimental demonstrations of p-DANTE sequences and comparisons with theory are presented.

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Section: Introductionmentioning

confidence: 99%

Pseudorandom selective excitation in NMR

Walls

Coomes

2011

Journal of Magnetic Resonance

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“…Switching magnetic equivalence by singlet-locking A detailed theoretical justification of how singlet-locking works makes use of average Hamiltonian theory [66] whose main equations are summarised in Appendix A.2. The purpose of the following demonstration is therefore to show that the first-order average Hamiltonian of the system does not contain any chemical shift contributions when an unmodulated radiofrequency field is applied on resonance (in the middle of the spectrum, i.e., for ω Σ = 0).…”

Section: Singlet-lockingmentioning

confidence: 99%

Singlet NMR methodology in two-spin-1/2 systems

Pileio

2017

Progress in Nuclear Magnetic Resonance Spectroscopy

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This paper discusses methodology developed over the past 12 years in order to access and manipulate singlet order in systems comprising two coupled spin-1/2 nuclei in liquid-state nuclear magnetic resonance. Pulse sequences that are valid for different regimes are discussed, and fully analytical proofs are given using different spin dynamics techniques that include product operator methods, the single transition operator formalism, and average Hamiltonian theory. Methods used to filter singlet order from byproducts of pulse sequences are also listed and discussed analytically. The theoretical maximum amplitudes of the transformations achieved by these techniques are reported, together with the results of numerical simulations performed using custom-built simulation code.

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“…A flexibility of NMR in handling spin dynamics comes from possibility of fast modulation of internal interactions by applying an external radio-frequency field. Such modulation allows "switching" interactions on and off or, more generally, creating average [15] or effective [16] Hamiltonians, which naturally do not exist. The scheme described below is based on creating an average Hamiltonian with non-degenerate eigenvalues and Bell states as its eigenstates.…”

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confidence: 99%