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arXiv:2604.04789

Quadrature-Symmetric PulsePol for Robust Quantum Control Beyond the Ideal Pulse Approximation

Mayur Jhamnani, Venkata SubbaRao Redrouthu, Jose P. Carvalho, Ethan Feldman, Anders B. Nielsen, Phani Kumar, Niels Chr. Nielsen, P. K. Madhu, Asif Equbal

quant-phcond-mat.otherSubmitted Apr 6, 2026• Announced Apr 7, 2026
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Abstract

PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.

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PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.
Abstract Hyperpolarization of nuclear spins is crucial for advancing nuclear magnetic resonance and quantum information technologies, as nuclear spins typically exhibit extremely low polarization at room temperature due to their small gyromagnetic ratios. A promising approach to achieving high nuclear spin polarization is transferring the polarization of electrons to nuclear spins. The nitrogen-vacancy (NV) center in diamond has emerged as a highly effective medium for this purpose, and various hyperpolarization 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 work, we present a novel polarization protocol and uncover a family of magic sequences for hyperpolarizing nuclear spins, with PulsePol emerging as a special case of our general approach. Notably, we demonstrate that some of these magic sequences exhibit significantly greater robustness compared to the PulsePol protocol in the presence of finite half π pulse duration of the protocol, Rabi and detuning errors. 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.
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.
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.
Nitrogen-vacancy (NV) center ensembles have the potential to improve a wide range of applications, including nuclear magnetic resonance spectroscopy at the microscale and nanoscale, wide-field magnetometry, and hyperpolarization of nuclear spins via the transfer of optically induced NV polarization to nearby nuclear spin clusters. These NV ensembles can be coherently manipulated with microwave cavities, that deliver strong and homogeneous drivings over large volumes. However, the pulse shaping for microwave cavities presents the challenge that the external controls and intracavity field amplitudes are not identical, leading to adverse effects on the accuracy of operations on the NV ensemble. In this paper, we introduce a method based on gradient ascent pulse engineering (GRAPE) to optimize external controls, resulting in robust pulses within the cavity while minimizing the effects of cavity ringings. The effectiveness of the method is demonstrated by designing both π and π / 2 pulses. These optimized controls are then integrated into a PulsePol sequence, where numerical simulations reveal a resilience to detunings five times larger than those tolerated by the sequence constructed using standard controls.
Defects in solid-state materials provide an ideal, robust platform for quantum sensing. To deliver maximum sensitivity, a large ensemble of noninteracting defects hosting quantum states with long coherence is required. Control of such an ensemble is challenging due to the spatial variation in both the defect energy levels and in any control field across a macroscopic sample. In this work, we experimentally demonstrate that we can overcome these challenges using Floquet theory and optimal control optimization methods to efficiently and coherently control a large defect ensemble, suitable for sensing. We apply our methods experimentally to a spin ensemble of up to $4\ifmmode\times\else\texttimes\fi{}{10}^{9}$ nitrogen-vacancy centers in diamond. By explicitly including the hyperfine interaction to the intrinsic 14N^{14}\mathrm{N}14N nuclear spin in the optimization, we design shaped microwave control pulses that can outperform conventional ($\ensuremath{\pi}$) pulses when applied to sensing schemes, with an improvement in the strength of ensemble response of between 11% and 78%. Through simulation of the ensemble dynamics, we shed light on the bandwidth limitations of large-ensemble reinitialization and propose alternative routes for further improvement.
Dynamical decoupling (DD) is a powerful method for controlling arbitrary open quantum systems. In quantum spin control, DD generally involves a sequence of timed spin flips (π rotations) arranged to either average out or selectively enhance coupling to the environment. Experimentally, errors in the spin flips are inevitably introduced, motivating efforts to optimize error-robust DD. Here we invert this paradigm: by introducing particular control "errors" in standard DD, namely, a small constant deviation from perfect π rotations (pulse adjustments), we show we obtain protocols that retain the advantages of DD while introducing the capabilities of quantum state readout and polarization transfer. We exploit this nuclear quantum state selectivity on an ensemble of nitrogen-vacancy centers in diamond to efficiently polarize the ^{13}C quantum bath. The underlying physical mechanism is generic and paves the way to systematic engineering of pulse-adjusted protocols with nuclear state selectivity for quantum control applications.