Semiclassical Lattice Effects on Interband Tunneling of a Two-state System

Abstract

Previously, we have shown that the transition probability of the Landau-Zener problem in periodic lattice systems becomes large by taking into account the nonlinearity of the energy spectra, compared with the probability by the conventional Landau-Zener formula. The enhancement comes from the nonlinearity peculiar to the periodic lattice system, and this effect from the lattice on transition action cannot be neglected in the transition process. In the present paper, we first give a brief review of the previous work, and construct the transfer matrix of the Landau-Zener problem by the semiclassical description for lattice systems. Next, we study a ladder lattice system and show that the transition action obtains a phase due to the nonlinearity. Then, we consider the double-passage problem of the ladder system within the semiclassical description. We find the oscillation of the probability by the transition phase by the lattice effect. This phase comes from the semiclassical analysis unlike the Stokes phase, and we show that the oscillation is mainly contributed by the transition phase by the lattice effect, when the hybridization of the ladder is strong.