Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling

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.

References in corpus (22)

• Nonlinearity-induced photonic topological insulator
• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Amplitude Spectroscopy of a Solid-State Artificial Atom
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• Decoherence in a scalable adiabatic quantum computer
• Landau-Zener Transition in Topological Acoustic Pumping
• Towards a Landau-Zener formula for an interacting Bose-Einstein condensate
• Correlated dynamics in a synthetic lattice of momentum states
• Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum Dots
• Commutability between Semiclassical Limit and Adiabatic Limit
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Resonant tunneling of Bose-Einstein condensates in optical lattices
• Occupation Statistics of a BEC for a Driven Landau-Zener Crossing
• Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Non-exponential tunneling due to mean-field induced swallowtails
• Nonlinear Landau-Zener-Stückelberg-Majorana problem
• Interaction induced Landau-Zener transitions
• Tunable nonlinear Landau-Zener tunnelings in a spin-orbit-coupled spinor Bose-Einstein condensate
• Suppressing excitations in the nonlinear Landau-Zener model