Dynamics and Stokes phases in multilevel non-Hermitian Landau-Zener transitions
Phys. Rev. A 114, 022212 – Published 19 August, 2026
DOI: https://doi.org/10.1103/8s6h-3nsq
Abstract
This study investigates the dynamics and phase of a nonreciprocal quantum multilevel spin system in Landau-Zener (LZ) transitions. Using Majorana's stellar representation, we analytically derive the solution for the LZ transition in a nonreciprocal quantum spin- model. Building on the results of the nonreciprocal two-level system, we construct and derive the expressions for the transition probabilities in multilevel systems, the evolution matrix for nonadiabatic evolution around exceptional points, and the Stokes phase generated by this process. Furthermore, taking a nonreciprocal quantum three-level model as an example, we confirm the validity of the analytically derived results for multilevel systems through numerical simulations, with particular emphasis on the differences and similarities between the non-Hermitian and Hermitian cases. Finally, the results show that for a nonreciprocal spin- system with an arbitrary number of levels, the nonadiabatic evolution matrix defined in the bare basis during the LZ transition can be obtained from the direct product of the two-level nonadiabatic evolution matrices and can be expressed in terms of a weighted Wigner matrix. Moreover, transitions between any two adjacent energy levels generate a Stokes phase of the same form as that in the two-level system, and the Stokes phase corresponds exactly to the two rotation angles in the plane of the rotation operator. As a concrete application, we map the three-level nonreciprocal LZ model to the three-band Su-Schrieffer-Heeger (SSH) model under an electric field and further extend this correspondence to general multiband SSH models. Our work provides a systematic and intuitive framework for analyzing non-Hermitian multilevel spin LZ dynamics, offering insights into nonreciprocal control, geometric phases, and nonadiabatic transitions in parity-time-symmetric and broader non-Hermitian quantum systems.
