Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling

TL;DR

This paper develops a comprehensive theory for anomalous Landau-Zener tunneling caused by nonlinear coupling, revealing a topological energy landscape and a universal fixed point that alters tunneling behavior in quantum systems.

Contribution

It introduces a novel framework for understanding nonlinear coupling effects on Landau-Zener tunneling, including a topological energy landscape and an exact tunneling probability formula.

Findings

Nonlinear coupling reshapes the adiabatic energy landscape.

A fixed point acts as a universal attractor, erasing initial state memory.

Derived an exact power-law formula for tunneling probability.

Abstract

We develop a general theory of Landau-Zener (LZ) tunneling in a two-level system with amplitude-dependent, sign-reversible nonlinear coupling, distinguishing it fundamentally from conventional on-site nonlinearity. Through a combination of analytical and phase-space analysis, we show that beyond a critical interaction strength, the nonlinear coupling fundamentally reshapes the adiabatic energy landscape, introducing a topological twisted and knotted structure. This structure leads to a complete breakdown of the standard exponential LZ formula, even in the adiabatic limit. Central to this anomalous behavior is the emergence of a black-hole-like fixed point, which acts as a universal attractor: upon traversing the critical region, all quantum trajectories converge to this fixed point, irreversibly erasing any memory of the initial state. From this fixed-point picture, we derive an exact analytical expression for the adiabatic tunneling probability, revealing a characteristic power-law dependence on both linear and nonlinear coupling strength. Our work establishes a paradigmatic framework for nonlinear-coupling-induced anomalous adiabaticity breaking and offers a universal mechanism for state control in driven quantum and wave systems.