SU(3) Landau-Zener interferometry

We propose a universal approach to the Landau-Zener problem in a three-level system. The problem is formulated in terms of Gell-Mann operators which generate SU(3) algebra and map the Hamiltonian on the effective anisotropic pseudospin 1 model. The vector Bloch equation for the density matrix describing the temporal evolution of the three-level crossing problem is also derived and solved analytically for the case where the diabatic states of the SU(3) Hamiltonian form a triangle. This analytic solution is in excellent quantitative agreement with the numerical solution of the Schrodinger equation for a 3-level crossing problem. The model demonstrates oscillation patterns which radically differ from the standard patterns for the two-level Landau-Zener problem. The triangle works as an interferometer and the interplay 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 in the triangle. These scales are related to the geometric size of the interferometer. The possibilities of the experimental realization of this effect in triple quantum dots and in two-well traps for cold gases are discussed. Copyright (C) EPLA, 2013