Archetypal Pulse Sequences

Archetype (noun); the original pattern or model of which all things of the same type are representations or copies.

The Merriam-Webster Dictionary

In many spin dynamical problems, I like to say there is an “archetypal” pulse sequence. The archetypal pulse sequence may be defined as the simplest possible way of achieving a unitary transformation from Operator A to Operator B. Typically the relevant operators are spin-state populations, so the behaviour expected under these sequences would correspond to the classic scenario of Rabi oscillations (i.e. motion from Population A to Population B, and back again). A recurrent motif in pulse sequence development is that the archetypal pulse sequence consists of nothing more than simple cw irradiation (perhaps preceded by a phase-shifted 90 pulse), whose amplitude is adjusted to satisfy a particular matching condition.

Examples of archetypal pulse sequences include:

1. The classic Hartmann-Hahn sequence for polarization transfer, which exchanges populations between spin(s) I and spin(s) S. The matching condition of the Hartmann-Hahn sequence is that the nutation frequency of the simultaneous driving field on the I and S spins coincides.
2. The NOVEL (nuclear orientation via electron spin-locking) sequence for DNP, which exchanges populations between electron (e) and nuclear (n) spins. The matching condition of NOVEL is that the nutation frequency of the driving field on the electron spins coincides with the Larmor frequency of the nuclear spins.
3. The SLIC (spin-lock induced crossing) sequence from the field of singlet NMR, which exchanges populations between (either of) the outer triplet states and the nuclear singlet state. The SLIC matching condition is that the nutation frequency of the driving field applied to a spin pair coincides with their homonuclear J-coupling.

All these pulse sequences are not that different:

This interpretation is quite useful. The archetypal pulse sequences are a direct map between fields of quantum dynamics that appear totally different at first sight. It immediately allows us to translate pulse sequences that were developed in one context, into another. Irrespective of the minutiae of the actual target effective Hamiltonian, and whatever populations are actually being exchanged, we can see that pulse sequences developed for, say, singlet NMR, may be adapted for DNP purposes, and vice versa.

In addition, archetypal pulse sequences possess interesting properties. For example, the SLIC sequence sets the bound on the fastest possible transfer from longitudinal magnetization to nuclear singlet order, which is just:

This basic but powerful correspondence was used by Nino Wili and myself as inspiration to adapt the PulsePol sequence (originally designed by Benedikt Tratzmiller of the Ulm group for optical DNP in NV centres) to the context of singlet NMR, and has also been noticed by other authors such as Pang et al. and Korzeczek et al..

As a pulse sequence designer, I (and the previous authors, evidently) think this is how we should be teaching these sequences to the coming generations of magnetic resonance. And I think that people in different fields (DNP, ssNMR, NV centres, solution-state singlet NMR, etc.) should talk to each other.