SU(3) Landau - Zener Interferometry

TL;DR

This paper develops a comprehensive SU(3) Landau-Zener theory for three-level quantum systems, revealing interference patterns like beats and steps, and proposes experimental setups in quantum dots to observe SU(3) symmetry effects.

Contribution

It introduces a novel SU(3) framework for Landau-Zener transitions, expressing Hamiltonians in terms of Gell-Mann matrices and analyzing interference phenomena in three-level systems.

Findings

Interference patterns depend on the geometric size of the interferometer.

Derived solutions to eight-dimensional Bloch equations for non-adiabatic transitions.

Proposed experimental realizations in triple quantum dots.

Abstract

We consider a general theory of Landau-Zener transitions in a three-level system. Based on a classification of three level crossings we express the Landau - Zener Hamiltonians in terms of two bases: i) spin S=1 SU(2) operators and ii) SU(3) Gell - Mann matrices. We show that the generic Hamiltonians being non-linear in terms of the SU(2) group generators become linear in the SU(3) basis. If the diabatic states of the SU(3) Landau - Zener Hamiltonian form a triangle, the interference between two paths results in formation of "beats" and "steps" pattern in the time-dependent transition probability. The characteristic time scales describing the "beats" and "steps" depend on a dwell time through the triangle. These scales are related to the geometric size of the interferometer. We formulate the SU(3) Landau - Zener problem in terms of Bloch dynamics of a unit vector and find a solution of eight-dimensional Bloch equations in the limit of a non-adiabatic transition. Possible experiments in triangular and linearly arranged triple quantum dots where Landau - Zener interferometry can be used for finding manifestations of SU(3) symmetry are discussed.