Environment-Induced Suppression of the Landau-Zener Transition Probability in a Driven Two-Level System

When the drive that causes the level crossing of a qubit is slow, the probability, P_LZ, of the Landau-Zener transition is close to 1. We show that, in this regime, which is most promising for applications, the noise due to coupling to the environment, reduces the average P_LZ. At the same time, the survival probability, 1-P_LZ, which is exponentially small for a slow drive, can be completely dominated by the noise-induced correction. On the physical level, the enhancement of the survival probability is due to the absorption of the “noise quanta”. This absorption can be calculated analytically by treating coupling to the environment perturbatively. The absorption is most efficient for the frequency components of noise of the order of the level repulsion, J. Thus, the survival probability is the function of the product, Jτ, where τ is the noise correlation function.