In situ learning-based spin engineering of pulsed dynamic nuclear polarization

Sci. Adv. 12, eaeh4467 (2026) · DOI: 10.1126/sciadv.aeh4467

License: CC BY 4.0.

Abstract

Pulsed dynamic nuclear polarization (DNP) is currently receiving substantial interest as a means to enhance the sensitivity of nuclear magnetic resonance (NMR) and magnetic resonance imaging by orders of magnitude. It has also received much attention as a central ingredient in many modalities of electron–spin–involved quantum sensing. Relative to spin engineering associated with NMR, the design of efficient pulsed DNP experiments with a broad experimental scope is challenged by large electron-nuclear spin systems, large electron–spin–involved interactions, and instrumental nonidealities and limitations. All of this may challenge traditional NMR-like theoretical and numerical pulse sequence engineering. Exploiting state-of-the-art instrumentation and taking advantage of the high sensitivity of DNP relative to NMR, we here demonstrate the use of combinations of Bayesian machine learning methods and constrained random walk procedures to design pulse sequences in situ, by experiments, directly on the spin systems responding to spectrometer instructions. For trityl and nitroxide samples, it is demonstrated that efficient broadband DNP pulse sequences can be designed in situ with experimental protocols benchmarked against in silico analogs.

Figures

22 panels with data across 3 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 2

• panel (aa): Absolute offset-averaged DNP enhancement $|\overline{\epsilon}|$ against sequence number for the 1000 sequences of the Monte Carlo optimization. Red dots match a DQ resonance ($\overline{\epsilon} > 0$), blue dots a ZQ resonance ($\overline{\epsilon} < 0$); the dashed line is the highest value so far. data.csv
• panel (ab): Accumulated nutation angle $\theta_{\mathrm{DNP}}$ (rad) against $t$ (ns), one line per sequence of the Monte Carlo optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; no colour bar); best sequence in black. Grey lines bound the allowed region (shaded in print); end ticks mark DQ (red) and ZQ (blue) resonances, $k_I$ labels not drawn. data.csv
• panel (ac): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) at the seven optimized offsets (dashed lines), one line per sequence of the Monte Carlo optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; colour bar not drawn); the best sequence in black. data.csv
• panel (ba): Absolute offset-averaged DNP enhancement $|\overline{\epsilon}|$ against sequence number for the 1000 sequences of the Bayesian optimization. Red dots match a DQ resonance ($\overline{\epsilon} > 0$), blue dots a ZQ resonance ($\overline{\epsilon} < 0$); the dashed line is the highest value so far. data.csv
• panel (bb): Accumulated nutation angle $\theta_{\mathrm{DNP}}$ (rad) against $t$ (ns), one line per sequence of the Bayesian optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; no colour bar); best sequence in black. Grey lines bound the allowed region (shaded in print); end ticks mark DQ (red) and ZQ (blue) resonances, $k_I$ labels not drawn. data.csv
• panel (bc): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) at the seven optimized offsets (dashed lines), one line per sequence of the Bayesian optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; colour bar not drawn); the best sequence in black. data.csv
• panel (ca): Absolute offset-averaged DNP enhancement $|\overline{\epsilon}|$ against sequence number for the 1000 sequences of the constrained Bayesian optimization. Red dots match a DQ resonance ($\overline{\epsilon} > 0$), blue dots a ZQ resonance ($\overline{\epsilon} < 0$); the dashed line is the highest value so far. data.csv
• panel (cb): Accumulated nutation angle $\theta_{\mathrm{DNP}}$ (rad) against $t$ (ns), one line per sequence of the constrained Bayesian optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; no colour bar); best sequence in black. Grey lines bound the allowed region (shaded in print); end ticks mark DQ (red) and ZQ (blue) resonances, $k_I$ labels not drawn. data.csv
• panel (cc): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) at the seven optimized offsets (dashed lines), one line per sequence of the constrained Bayesian optimization, coloured by its $\overline{\epsilon}$ (red positive, blue negative, pale near zero; colour bar not drawn); the best sequence in black. data.csv
• panel (d): Normalized EPR signal of trityl OX063 against $\gamma_{\mathrm{exp}} B_0$ (GHz). Vertical lines mark the resonance and the MW carrier at $-60$ MHz offset (drawn in print as arrows, with an arrow for the electron offset between them). data.csv
• panel (e): Absolute offset-averaged enhancement $|\overline{\epsilon}|$ against sequence number for the 2000 sequences of the constrained Bayesian optimization of a 24-pulse transfer element. The open circle marks the sequence with the best offset profile when repeated at finer offset resolution. data.csv
• panel (f): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) for the 24-pulse BayesOpt sequence marked in (E), compared with NOVEL, PLATO and cRW-OPT1 (trityl OX063 in glycerol-d8). data.csv

Fig. 3

• panel (a): Absolute offset-averaged enhancement $|\overline{\epsilon}|$ against sequence number for the 1000 evaluations of the Bayesian in situ optimization of a four-pulse excitation sequence followed by cRW-OPT1. The dashed line is the highest value so far; the open circle marks the best sequence. data.csv
• panel (b): Best four-pulse excitation sequence of (A): Rabi frequency $\omega_1/(2\pi)$ (MHz, grey, left axis) and phase $\phi$ (rad, red, right axis) against pulse number. data.csv
• panel (c): Experimental $|\overline{\epsilon}|$ against simulated $|\overline{\langle I_z \rangle}|$ for all sequences evaluated in (A). Dashed lines mark the best sequence, as shown in (D) and (E). data.csv
• panel (d): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) for the best excitation sequence of (A) (glycerol-d5): green dots, the experiment repeated on a finer offset grid; crosses, the enhancements found during optimization; dashed line, their average. data.csv
• panel (e): Simulated proton polarization $\langle I_z \rangle$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) for the best excitation sequence followed by cRW-OPT1 (solid line); crosses, the simulated transfer at the optimized offsets; dashed line, their average. data.csv
• panel (f): DNP enhancement $\epsilon$ against electron-spin offset $\Delta\omega_S/(2\pi)$ (MHz) for cRW-OPT1 after a hard excitation pulse with its carrier moved with the offset or fixed at $\Delta\omega_S = 0$, and after the Bayesian excitation sequence moved with the offset (glycerol-d8). data.csv

Fig. 4

• panel (a): Absolute DNP enhancement $|\epsilon|$ against sequence number for the 2000 evaluations of the Monte Carlo optimization of excitation and transfer pulses (2 mM 4-Oxo-TEMPO). The dashed line is the highest value so far. data.csv
• panel (b): Absolute DNP enhancement $|\epsilon|$ against sequence number for the 2000 evaluations of the unconstrained Bayesian optimization of excitation and transfer pulses (2 mM 4-Oxo-TEMPO). The dashed line is the highest value so far; the open circle marks the best sequence. data.csv
• panel (c): Best sequence of the Bayesian optimization in (B): Rabi frequency $\omega_1/(2\pi)$ (MHz, grey, left axis) and phase $\phi$ (rad, red, right axis) against pulse number: pulses 1 to 4 excitation, 5 to 12 transfer. data.csv
• panel (d): DNP enhancement $|\epsilon|$ against buildup time $t_{\mathrm{DNP}}$ (s) for the best sequence of the Bayesian optimization and for a hard excitation pulse followed by a constant-amplitude spin-lock pulse; the cross is the enhancement measured during the optimization at 8 s buildup. data.csv

Fig. 5

Illustrative figure, no extractable data. Shown in the paper PDF.

Cite

Filip V. Jensen, José P. Carvalho, Nino Wili, Asbjørn Holk Thomsen, David L. Goodwin, Lukas Trottner, Claudia Strauch, Anders Bodholt Nielsen, Niels Chr. Nielsen. In situ learning-based spin engineering of pulsed dynamic nuclear polarization. Sci. Adv. 12, eaeh4467 (2026). https://doi.org/10.1126/sciadv.aeh4467

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