Landau–Zener transition with energy-dependent decay rate of the excited state

Abstract

A remarkable feature of the Landau–Zener transition is insensitivity of the survival probability to the decay rate, τ−1, of the excited state. Namely, the probability for a particle which is initially (at t→−∞) in the ground state to remain at t→∞ in the same state is insensitive to τ−1 which is due to e.g. coupling to continuum (Akulin and Schleich, 1992). This insensitivity was demonstrated for the case when the density of states in the continuum is energy-independent. We study the opposite limit when the density of states in the continuum is a step-like function of energy. As a result of this step-like behavior of the density of states, the decay rate of a driven excited level experiences a jump as a function of time at certain moment t0. We take advantage of the fact that the analytical solution at t<t0 and at t>t0 is known. We show that the decay enters the survival probability when t0 is comparable to the transition time.