Landau-Zener transitions in an open multilevel quantum system

TL;DR

This paper investigates Landau-Zener transitions in multilevel quantum systems coupled to an environment, revealing that environmental coupling transforms transitions into sequences of smaller ones, with final state probabilities unaffected when starting from ground states.

Contribution

It extends Landau-Zener theory to open multilevel systems, showing how environment coupling modifies transition dynamics and providing an intuitive understanding of these processes.

Findings

Ground state occupation probabilities remain unaffected by environment coupling.

Environmental interaction converts transitions into sequences of smaller transitions.

Sequence duration increases with stronger system-environment coupling.

Abstract

We consider the Landau-Zener problem for a multilevel quantum system that is coupled to an external environment. In particular, we consider a number of cases of three-level systems coupled to a harmonic oscillator that represents the external environment. We find that, similar to the case of the Landau-Zener problem with a two-level system, when the quantum system and the environment are both initially in their ground states the probability that the system remains in the same quantum state is not affected by the coupling to the environment. The final occupation probabilities of the other states are well described by a common general principle: the coupling to the environment turns each Landau-Zener transition process in the closed system into a sequence of smaller transitions in the combined Hilbert space of the system and environment, and this sequence of transitions lasts a total duration that increases with increasing system-environment coupling strength. These results provide an intuitive understanding of Landau-Zener transitions in open multilevel quantum systems.