Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble

We study the quantum dynamics of a non-interacting spin ensemble under the effect of a reservoir by applying the framework of the non-Hermitian Hamiltonian operators. Theoretically, the two-level model describes the quantum spin system and the Bloch vector to establish the dynamical evolution. Experimentally, phosphorous ($^{31}$P) nuclei with spin $I=1/2$ are used to represent the two-level system and the magnetization evolution is measured and used to compare with the theoretical prediction. At room temperature, the composite dynamics of the radio-frequency pulse plus field inhomogeneities (or unknown longitudinal fluctuations) along the $z$-axis transform the initial quantum state and drives it into a mixed state at the end of the dynamics. The experimental setup shows a higher accuracy when compared with the theoretical prediction (>98\%), ensuring the relevance and effectiveness of the non-Hermitian theory at a high-temperature regime.