Preprints
https://doi.org/10.5194/mr-2022-9
https://doi.org/10.5194/mr-2022-9
 
16 May 2022
16 May 2022
Status: this preprint is currently under review for the journal MR.

Visualization of Spin Dynamics in Coupled Nuclear Multispin Systems

Jingyan Xu1,2, Dmitry Budker1,2,3, and Danila A. Barskiy1,2 Jingyan Xu et al.
  • 1Institut für Physik, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
  • 2Helmholtz Institut Mainz, 55128 Mainz, Germany; GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
  • 3University of California at Berkeley, California 94720-7300, USA

Abstract. Since the dawn of quantum mechanics ways to visualize spins and their interactions attracted attention of researchers and philosophers of science. Angular momentum probability (AMP) surfaces are known for visualizing density matrices; a plotted surface represents probability of finding maximum projection of angular momentum along any direction in space. While AMP surfaces visually reveal symmetries of density matrices which directly translate to measured properties, they focus solely on one total-angular-momentum manifold, neglecting interaction between different manifolds often encountered in the NMR of multispin systems. In this work, we extend applicability of this visualization method and introduce its extension, angular momentum coherence (AMC) surface approach. Three examples of nuclear spin dynamics in two-spin systems are presented and visualized using the AMP/AMC surfaces: (I) spin-lock induced crossing (SLIC) sequence with initial state being the singlet state between two spins; (II) interplay between chemical exchange and spin dynamics during the high-field signal amplification by reversible exchange (SABRE) experiment; (III) zero- to ultralow-field (ZULF) NMR experiment in the presence of magnetic field applied perpendicular to the sensitive axis of the detector. The presented visualization technique extends applicability of AMP surfaces to coupled multispin systems and will facilitate intuitive understanding of spin dynamics during complex NMR experiments as exemplified here by the considered cases. The temporal sequences (“the movies”) of such surfaces show phenomena like interconversion of polarization moments (Auzinsh et al., 2010) and, as particularly relevant in NMR and demonstrated here, polarization transfer between different spins. Such effects are difficult to grasp by looking at (time-dependent) numerical values of density-matrix elements.

Jingyan Xu et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on mr-2022-9', Andrey Pravdivtsev, 20 May 2022
    • CC2: 'Reply on CC1', Danila Barskiy, 27 May 2022
  • RC1: 'Comment on mr-2022-9', Anonymous Referee #1, 25 May 2022
    • AC1: 'Reply on RC1', Danila Barskiy, 27 May 2022
  • RC2: 'Comment on mr-2022-9', Malcolm Levitt, 26 May 2022
    • AC2: 'Reply on RC2', Danila Barskiy, 04 Jun 2022
  • RC3: 'Comment on mr-2022-9', Malcolm Levitt, 29 May 2022
  • CC4: 'Comment on mr-2022-9', Tom Barbara, 31 May 2022
    • CC5: 'Reply on CC4', Tom Barbara, 01 Jun 2022
    • AC3: 'Reply on CC4', Danila Barskiy, 04 Jun 2022
  • RC4: 'Comment on mr-2022-9', Steffen Glaser, 01 Jun 2022
  • CC6: 'Comment on mr-2022-9', Balint Koczor, 06 Jun 2022
  • EC1: 'Comment on mr-2022-9', Geoffrey Bodenhausen, 11 Jun 2022
  • EC2: 'Comment on mr-2022-9', Geoffrey Bodenhausen, 11 Jun 2022

Jingyan Xu et al.

Jingyan Xu et al.

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Short summary
We extend an approach for visualizing dynamics of quantum spin systems based on angular momentum probability (AMP) surfaces to visualizing coherences via angular momentum coherence (AMC) surfaces. AMP/AMC surfaces conveniently represent symmetries of density matrices and allow spotting their presence (orientation, alignment, etc.) or absence even when direct analysis of density matrices is not obvious. We apply novel visualization approach to represent relevant cases of 2-spin system dynamics.