Longitudinal Pulsed Dynamic Nuclear Polarization Transfer via Periodic Optimal Control

TL;DR

Broadband DNP has traditionally relied on excitation-pulse methods with limited bandwidth. The LOOP approach uses periodic, phase-modulated pulses optimized by replicated state-to-state optimal control to induce longitudinal polarization transfer via effective $z$-rotations, achieving DNP bandwidths approaching 100 MHz at a peak MW field of 32 MHz. Simulations and X-band experiments on a two-spin electron-nucleus pair show LOOP sequences offer high transfer efficiency and strong resilience to microwave offsets and inhomogeneity, with LOOP-1 delivering higher enhancements than NOVEL. This excitation-pulse-free, longitudinal transfer framework expands the practical reach of DNP—enabling low-field operation, potential integration with MAS NMR dipolar recoupling, and applications in quantum sensing.

Abstract

Taking inspiration from NMR spectroscopy, periodic irradiation schemes have recently shown remarkable performance when implemented into pulsed dynamic nuclear polarization (DNP) sequences. This has prompted considerable interest in development of broadband pulsed DNP sequences utilizing such schemes. On this background, most efforts have focused on solid-state NMR like transverse spin-locked pulse sequences whose performance in DNP applications may be compromised by the broadband capabilities of the initial excitation pulse. Leveraging the flexibility and robustness of optimal control theory combined with underlying insights from effective Hamiltonian theory, we present a new family of broadband DNP pulse sequences, termed LOOP (Longitudinally Optimized with Overarching Periodicity), that alleviates the excitation-pulse challenge by accomplishing longitudinal polarization transfer. These sequences define robust single-spin effective $z$ rotations, with impressive compensation towards microwave field inhomogeneity, and are capable of delivering DNP transfer with bandwidths exceeding 100 MHz, while employing a peak microwave field amplitude of only 32 MHz, at an external magnetic field of 0.35 T.

Figures (5)

• Figure 1: Schematic representation of pulsed DNP sequences used in this work. (a) Pulse sequence scaffold used to measure the DNP enhancement, consisting of $^1$H saturation train, followed by the DNP block where the total buildup time is defined by $T_\text{DNP}=h\cdot t_\text{rep}$, and ending on $^1$H spin polarization readout with a solid-echo sequence. (b) Pulse sequences used for the DNP contact: NOVEL, periodic transverse spin-lock, and periodic longitudinal schemes.
• Figure 2: Simulated LOOP DNP transfer profiles as a function of the electron spin offset ($\Delta\omega_\text{S}/(2\pi)$) and deviation from the nominal MW field amplitude ($\omega_{MW}/\omega_{MW}^\text{max}$). The simulations assumed a powder-averaged e$^-$-$^1$H two-spin system with an anisotropy of the hyperfine coupling of $T/(2\pi)$ = 0.8676 MHz (corresponding to an inter-spin distance of $r_\text{eH}$ = 4.5 Å in a point-dipole model) and a static magnetic field corresponding to a proton Larmor frequency of $-14.8$ MHz (approximately 0.35 T).The $t_\text{contact}$ was defined to maximize the integrated DNP transfer bandwidth between $-30$ and 30 MHz. In panels (a)-(e), the transfer profiles are shown as a function of electron spin offset and MW field amplitude. In panel (f), the 1D traces, taken at the nominal MW field strength, $\omega_{MW}^\text{max}/(2\pi)=32$ MHz, are shown.
• Figure 3: Experimental DNP transfer profiles ($\epsilon_\text{P}$) obtained at X-band on a sample of trityl (OX063) in a water/glycerol mixture at 80K following the pulse sequence represented in Fig. \ref{['fig:fig1']}, shown above, and the following transverse spin-locked sequences: NOVEL, PLATO, and CRW-1, shown below. (a) DNP transfer profiles as a function of electron spin offset ($\Delta\omega_\text{S}/(2\pi)$) recorded at $t_\text{DNP}=5$ s. To facilitate comparison, faded representations of the NOVEL and LOOP-5 DNP transfer profiles were shown in the LOOP and transverse spin-locked subplots, respectively. (b) DNP transfer profiles as a function of pumping time $(t_\text{DNP})$ recorded at $\Delta\omega_\text{S}/(2\pi)=0$ MHz. The experimental data was fit to the exponential function: $\epsilon_\text{P}(t_\text{DNP})=\epsilon_\text{max}[1-\exp(-t_\text{DNP}/T_\text{B})]$, where $T_\text{B}$ defines the characteristic buildup time. All fitted buildup times were approximately 8 s (cf. Tab. II of the SI). The experimental DNP transfer profiles were all phased so that a positive enhancement occurs at $\Delta\omega_\text{S}/(2\pi)=0$ MHz.
• Figure S1: $T_1$ relaxation times. (a) Inversion recovery data for electronic spins. $T_{1,e}$ determined via an exponential fit:$I/I_\infty(t)=[1-2\exp(-t/T_{1,e})]$. (b) Nuclear polarization after DNP. $T_{1,n}$ determined via an exponential fit: $\epsilon_\text{p}(t)=\epsilon_\text{max}\exp(-t/T_{1,n})]$. See the main text for experimental details.
• Figure S2: Experimental DNP transfer profiles ($\epsilon_\text{P}$) for NOVEL, PLATO, and cRW-OPT1 pulse sequences as a function of electron spin offset ($\Delta\omega_\text{S}/(2\pi)$) recorded at $t_\text{DNP}=5$ s, obtained at X-band on a sample of trityl (OX063) in a water/glycerol mixture at 80 K, following the pulse sequence represented in Fig. \ref{['fig:fig1']} of the main text. In the left panel, the initial electron-spin $\pi/2$ pulse follows the offset of the DNP pulse sequence element, whereas in the right panel, it is on-resonance throughout the offset scan of the DNP sequence.