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

TL;DR

This paper investigates how an energy-dependent, step-like decay rate affects the Landau-Zener transition, revealing that decay influences survival probability when the decay rate jump coincides with the transition time.

Contribution

It extends the understanding of Landau-Zener transitions by analyzing the impact of energy-dependent decay rates with step-like density of states.

Findings

Decay affects survival probability when decay rate jump aligns with transition time.

Analytical solutions are used to show the influence of energy-dependent decay.

The insensitivity of survival probability is broken by energy-dependent decay rates.

Abstract

A remarkable feature of the Landau-Zener transition is insensitivity of the survival probability to the decay rate, of the excited state. Namely, the probability for a particle, which is initially in the ground state, to remain in the same state is insensitive to decay, which is due to e.g. coupling to continuum [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (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 t_0. We take advantage of the fact that the analytical solution at t<t_0 and at t>t_0 is known. We show that the decay enters the survival probability when t_0 is comparable to the transition time.