Crossing time in the Landau-Zener quantum dynamics in a super Ohmic environment

TL;DR

This paper investigates how a super Ohmic environment affects the Landau-Zener transition in a quantum two-state system, revealing dependencies on coupling strength and bath cut-off frequency, and providing insights for controlling quantum dynamics.

Contribution

It introduces a detailed analysis of Landau-Zener dynamics under super Ohmic dissipation, highlighting the impact of bath spectral properties and proposing accurate modeling approaches.

Findings

Relaxation influences the crossing time window around the avoided crossing.

Crossing time depends on system-bath coupling and bath spectral cut-off frequency.

Nonequilibrium Bloch equations are accurate at weak coupling.

Abstract

We study the dynamics of a quantum two state system driven through an avoided crossing under the influence of a super Ohmic environment, i.e. a longitudinal as well as a transversal one. The crossing time window, in which relaxation influences the dynamics, is centered around the avoided crossing. We determine the dynamics and the Landau-Zener probability employing the numerical exact quasi-adiabatic path integral. At weak coupling we show that the numerically less demanding nonequilibrium Bloch equations provide an accurate description. The crossing time depends strongly not only on the system-bath coupling strength but also on the bath spectral cut-off frequency in contrast to the situation in an Ohmic bath. Our results enable to design quantitative protocols which drive quantum systems out of the influence range of relaxation.