Suppression of the Landau-Zener transition probability by weak classical noise
Rajesh K. Malla, Eugene G. Mishchenko, M. É. Raǐkh · Physical review. B./Physical review. B · 2017
When the drive, which causes the level crossing in a qubit, is slow, the probability ${P}_{LZ}$ of the Landau-Zener transition is close to 1. In this regime, which is most promising for applications, the noise due to the coupling to the environment reduces the average ${P}_{LZ}$. At the same time, the survival probability, $1\ensuremath{-}{P}_{LZ}$, which is exponentially small for a slow drive, can be completely dominated by noise-induced correction. Our main message is that the effect of weak classical noise can be captured analytically by treating it as a perturbation in the Schr\"odinger equation. This allows us to study the dependence of the noise-induced correction to ${P}_{LZ}$ on the correlation time of the noise. As this correlation time exceeds the bare Landau-Zener transition time, the effect of noise becomes negligible. On the physical level, the mechanism of enhancement of the survival probability can be viewed as an absorption of the ``noise quanta'' across the gap. With characteristic energy of the quantum governed by the noise spectrum, the slower the noise is, the lower the number of quanta for which absorption is allowed energetically is. We consider two conventional realizations of noise: Gaussian noise and telegraph noise.