Nonlinear Landau-Zener-Stückelberg-Majorana problem with non-Hermitian models

作者：Y. Cao, T. F. Xu · 发表于：Physical Review A · 年份：2024 · DOI：10.1103/physreva.109.012622 · 被引用次数：4 · 研究领域：Quantum Mechanics and Non-Hermitian Physics、Quantum chaos and dynamical systems、Nonlinear Photonic Systems

We study nonlinear Landau-Zener-St\"uckelberg-Majorana (LZSM) tunneling with a $\mathcal{PT}$-symmetric potential, which can be converted to a non-Hermitian nonlinear two-level model by a two-mode approximation. Then, we construct an equivalent Hermitian model through a transformation, verify that the tunneling probabilities obtained by the two models are consistent, and comprehensively analyze the effect of the gain-dissipation term on tunneling. In addition, due to the gain-dissipation properties, the total population density of the non-Hermitian model is no longer a conserved quantity, which will increase or decay to a fixed value as the model evolves. Finally, we prove that the spatial inversion symmetry breaking of the Hamiltonian leads to nonreciprocal tunneling, and the numerical simulation results confirm our analysis. These studies provide alternative ideas to study the nonlinear dynamics of non-Hermitian systems in the future.