Eigenstate versus Zeeman-based approaches to the solid-effect

TL;DR

This paper compares Zeeman and eigenstate-based perturbation approaches to the solid effect in dynamic nuclear polarization, revealing that the Zeeman approach underestimates nuclear polarization due to leakage transitions.

Contribution

It derives effective Liouville equations for both approaches from first principles and analyzes their differences in predicting nuclear polarization.

Findings

Zeeman approach underestimates nuclear polarization.

Leakage transitions cause discrepancies in the Zeeman basis.

Eigenstate approach provides more accurate polarization estimates.

Abstract

The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation which describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.