Adiabaticity in nonreciprocal Landau-Zener tunneling

TL;DR

This paper explores how nonreciprocal coupling and nonlinear interactions influence adiabatic Landau-Zener tunneling in a two-level quantum system, revealing conditions for adiabaticity breakdown and precise tunneling probability predictions.

Contribution

It provides analytical and classical trajectory-based methods to predict adiabatic tunneling probabilities in non-Hermitian, nonlinear two-level systems, highlighting the effects of nonreciprocity and exceptional points.

Findings

Adiabatic tunneling probabilities can be predicted by classical action at EPs.

Nonlinear interactions can be suppressed in strong nonreciprocity regimes.

Adiabaticity can break down, leading to nonzero tunneling probabilities even in slow evolution.

Abstract

We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.