Role of quantum coherence in chirped dynamic nuclear polarization.

Dynamic Nuclear Polarization (DNP) is transforming nuclear magnetic resonance and MRI by significantly enhancing sensitivity through the transfer of polarization from electron spins to nuclear spins via microwave irradiation. However, the use of monochromatic continuous-wave irradiation limits the efficiency of DNP for systems with heterogeneous, broad electron paramagnetic resonance lines. Broadband techniques such as chirp irradiation offer a potential solution, particularly for Solid Effect (SE) DNP in such cases. Despite its widespread use, the role of quantum coherence generated during chirp irradiation remains unclear, even though it is a key factor in determining the maximum achievable DNP efficiency. In this work, we use density matrix formalism to provide a comprehensive understanding of the quantum coherence generated during non-adiabatic passages through electron-nucleus double-quantum (DQ) and zero-quantum (ZQ) SE transitions and their impact on Integrated Solid Effect (ISE) DNP under chirp irradiation. Our analysis employs fictitious product-operator bases to trace the evolution of electron-nucleus coherence leading to integrated or differentiated SE. We also explore the role of decoherence in maximizing chirped DNP in microwave power or nutation frequency limited scenarios. These findings provide an understanding of the role of coherence generated during pulsed DNP and magic-angle spinning DNP at different temperature ranges. Our results reveal that quantum coherences generated during non-adiabatic passages critically determine whether the chirped DNP process yields ISE or differential solid effect. By analyzing the evolution of the density matrix in DQ and ZQ subspaces, we show how coherence generation and its decay through decoherence play a decisive role in shaping the net DNP enhancement.