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arXiv:2602.08883

Error compensation without a time penalty: robust spin-lock-induced crossing in solution NMR

Mohamed Sabba, Christian Bengs, Urvashi D. Heramun, Malcolm H. Levitt

quant-phphysics.chem-phSubmitted Feb 9, 2026• Announced Feb 10, 2026
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Abstract

A modification of the widely-used spin-lock-induced crossing (SLIC) procedure is proposed for the solution nuclear magnetic resonance (NMR) of strongly coupled nuclear spin systems, including singlet NMR and parahydrogen-enhanced hyperpolarised NMR experiments. The compensated-SLIC (cSLIC) scheme uses a repetitive sequence where the repeated element employs two different radiofrequency field amplitudes. Effective compensation for deviations in the radiofrequency field amplitude is achieved without increasing the overall duration of the SLIC sequence. The advantageous properties of cSLIC are demonstrated by numerical simulations and by representative experiments.

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A modification of the widely-used spin-lock-induced crossing (SLIC) procedure is proposed for the solution nuclear magnetic resonance (NMR) of strongly coupled nuclear spin systems, including singlet NMR and parahydrogen-enhanced hyperpolarised NMR experiments. The compensated-SLIC (cSLIC) scheme uses a repetitive sequence where the repeated element employs two different radiofrequency field amplitudes. Effective compensation for deviations in the radiofrequency field amplitude is achieved without increasing the overall duration of the SLIC sequence. The advantageous properties of cSLIC are demonstrated by numerical simulations and by representative experiments.
A family of double-quantum excitation schemes is described for the solution nuclear magnetic resonance (NMR) of near-equivalent spin-1/2 pairs. These new methods exploit the spinor behaviour of 2-level systems, whose signature is the change of sign of a quantum state upon a 2π2π2π rotation. The spinor behaviour is used to manipulate the phases of single-quantum coherences, in order to prepare a double-quantum precursor state which is rapidly converted into double-quantum coherence by a straightforward π/2π/2π/2 rotation. One set of spinor-based methods exploits symmetry-based pulse sequences, while the other set exploits SLIC (spin-lock-induced crossing), in which the nutation frequency under a resonant radiofrequency field is matched to the spin-spin coupling. A variant of SLIC is introduced which is well-compensated for deviations in the radiofrequency field amplitude. The methods are demonstrated by performing double-quantum-filtered 19^{19}19F NMR on a molecular system containing a pair of diastereotopic 19^{19}19F nuclei. The new methods are compared with existing techniques.
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 zzz 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.
Recently, Pang et al reported a novel polarization transfer scheme applicable to three-spin systems, whereby a rotating-frame NMR analogue of the cross effect could transfer polarization between; e.g., two 13Cs and an 15N in a single crystal. The present work furthers this scheme to the case of powder NMR under magic angle spinning (MAS) conditions, as well as to solution NMR. It is found that in all such cases a second-order average Hamiltonian can transfer polarization between non-equivalent, coupled abundant spins (e.g., two 1Hs) prepared in anti-longitudinal magnetization states, and the spin-locked magnetization of a rare spins (e.g., one 13C). The average Hamiltonian for such three-spin (S1-S2) to I transfer was derived for both liquids and solids, and found in good quantitative agreement with numerical simulations and experiments. At an optimal transfer condition whereby an I-spin RF irradiation field matches the S1-S2 chemical-shift-difference, a maximum polarization enhancement equal to the ratio of gyromagnetic ratios is achieved; as explained and demonstrated in the study, ca. half of this can be effectively obtained for I = 13C in powdered solids and in multi-spin systems in solutions. All such processes display an oscillatory nature, meaning that the transverse spin-locked polarization of a rare spin can become anti-longitudinal magnetization of abundant spins -without ever pulsing on the latter. The roles played by many-body interactions, RF inhomogeneities, and interferences of other coherences during the execution of these novel forms of cross-polarization were investigated, and are exemplified with experiments and simulations.
Nuclear spin qubits in silicon are well-isolated from their environment. Consequently, they have very long lifetimes and low sensitivity to noise, but this also suggests that control and measurement is challenging. We introduce electron pair interferometry (EPI), a protocol to overcome this challenge and maintain robustness to noise. EPI is implemented using an array of quantum dots with isoelectronic nuclear spin qubits located in the dots. A pair of electrons are initialized into a singlet ground state, split apart, and shuttled to the dots containing nuclear spin qubits. We show it is possible to coherently transfer the parity of the nuclei onto the measurable state of singlet/triplet-encoded electrons. Global nuclear magnetic resonance (NMR) can be used to change bases and implement dynamical decoupling (DD). Combined with selective hyperfine-induced ZπZ_πZπ​ rotations, our gate set is complete for universal quantum computation, tailored to Calderbank-Shor-Steane (CSS) quantum error correction, and robust to noise. We discuss very low sensitivity to charge noise and study the sensitivity to both DC and AC magnetic field inhomogeneity which depends strongly on their relative strengths.
The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.
Hyper-polarization of nuclear spins is crucial for advancing nuclear magnetic resonance (NMR) and quantum information technologies, as nuclear spins typically exhibit extremely low polarization at room temperature due to their small gyro-magnetic ratios. A promising approach to achieving high nuclear spin polarization is transferring the polarization of electron to nuclear spin. The nitrogen-vacancy (NV) center in diamond has emerged as a highly effective medium for this purpose, and various hyper-polarization protocols have been developed. Among these, the pulsed polarization (PulsePol) method has been extensively studied due to its robustness against static energy shifts of the electron spin. In this study, we introduce a sequential polarization protocol and identify a series of magic and digital sequences for hyper-polarizing nuclear spins. Notably, we demonstrate that some of these magic sequences exhibit significantly greater robustness compared to the PulsePol protocol in the presence of finite half πππ pulse duration of the protocol. This enhanced robustness positions our protocol as a more suitable candidate for hyper-polarizing nuclear spins species with large gyromagnetic ratios and also ensures better compatibility with high-efficiency readout techniques at high magnetic fields. Additionally, the generality of our protocol allows for its direct application to other solid-state quantum systems beyond the NV center.