Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory

Abstract

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly-looking models belong to different topological classes.

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Cited by in corpus (15)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots
• Generalized Adiabatic Impulse Approximation
• Nonlinear Landau-Zener-Stückelberg-Majorana problem
• Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
• Single spin Landau-Zener-Stückelberg-Majorana interferometry of Zeeman-split states with strong spin-orbit interaction in a double quantum dot
• Dynamics of dissipative Landau-Zener transitions in an anisotropic three-level system
• Controlling qubit-oscillator systems using linear parameter sweeps
• Controllable single spin evolution at sub-harmonics of electric dipole spin resonance enhanced by four-level Landau-Zener-St{ü}ckelberg-Majorana interference
• Nonadiabatic dissociation of molecular Bose-Einstein condensates: competition between chemical reactions
• Landau-Zener transition between two quantum dots coupled by resonant tunneling
• Nonadiabatic transition at a band-touching point
• Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models
• Graph-theoretical search for integrable multistate Landau-Zener models
• Competing Bosonic Reactions: Insight from Exactly Solvable Time-Dependent Models