Adiabatic Landau–Zener transitions at avoided level crossings with fast noise

Abstract

Effects of a fast classical noise on adiabatic Landau–Zener (LZ) transitions between the (2S+1) Zeeman multiplets (diabatic states) of an arbitrary spin S at an avoided level crossing are investigated. The spin system is simultaneously coupled to a slow regular magnetic field and a fast random field with Gaussian realizations. In the longitudinal direction, the magnetic field changes its sign at the degeneracy point (and is unbounded at large positive and negative times t=±∞ far from the degeneracy point) while in its single transverse direction, it remains of constant amplitude. The noise is considered in the limit where its characteristic correlation time (decay time) is small enough compared to the characteristic time of adiabatic LZ transitions. With these considerations, the condition for adiabatic evolution allows us to analytically evaluate the populations of diabatic levels and coherence factors. The study is first implemented for two- (S=1/2) and three- (S=1) state systems and finally extended to arbitrary S. A numerical study is implemented allowing us to check/confirm the range of validity of our analytical solutions. We found a satisfactory quantitative agreement between numerical and analytical data.