Landau-Zener transition in a two-level system coupled to a single highly-excited oscillator

TL;DR

This paper provides an analytical study of Landau-Zener transitions in a two-level quantum system coupled to a highly excited oscillator, revealing how oscillator dynamics influence transition probabilities in different regimes.

Contribution

It offers an analytical solution for transition probabilities at high oscillator excitation and clarifies the effects of slow and fast oscillators on the transition process.

Findings

Slow oscillator renormalizes drive velocity, affecting transition probability.

Fast oscillator renormalizes transition matrix element, leading to non-monotonic probability dependence.

Transition probability is suppressed overall in the presence of coupling.

Abstract

Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the transition probability is possible when the oscillator is highly excited, i.e. at high temperatures. Then the relative change of the excitation level of the oscillator in the course of the transition is small. The physical picture of the transition in the presence of coupling to the oscillator becomes transparent in the limiting cases of slow and fast oscillator. Slow oscillator effectively renormalizes the drive velocity. As a result, the transition probability either increases or decreases depending on the oscillator phase. The net effect is, however, the suppression of the transition probability. On the contrary, fast oscillator renormalizes the matrix element of the transition rather than the drive velocity. This renormalization makes the transition probability a non-monotonic function of the coupling amplitude.