Fast quantum noise in Landau-Zener transition

TL;DR

This paper analytically investigates how fast quantum noise influences Landau-Zener transitions in a two-state system, revealing distinct effects of longitudinal and transverse noise on transition probabilities and coherence.

Contribution

It provides a microscopic derivation of the master equation for fast quantum noise and solves it analytically across various parameters, highlighting the different impacts of longitudinal and transverse noise.

Findings

Fast transverse noise affects transition probability over longer times.

Longitudinal noise's effect is limited by the Landau-Zener timescale.

Correlation between noises can enhance survival probability.

Abstract

We show by direct calculation starting from a microscopic model that the two-state system with time-dependent energy levels in the presence of fast quantum noise obeys the master equation. The solution of master equation is found analytically and analyzed in a broad range of parameters. The fast transverse noise affects the transition probability during much longer time (the accumulation time) than the longitudinal one. The action of the fast longitudinal noise is restricted by the shorter Landau-Zener time, the same as in the regular Landau-Zener process. The large ratio of time scales allows solving the Landau-Zener problem with longitudinal noise only, then solving the same problem with the transverse noise only and matching the two solutions. The correlation of the longitudinal and transverse noise renormalizes the Landau-Zener transition matrix element and can strongly enhance the survival probability, whereas the transverse noise always reduces it. Both longitudinal and transverse noise reduce the coherence. The decoherence time is inverse proportional to the noise intensity. If the noise is fast, its intensity at which the multi-quantum processes become essential corresponds to a deeply adiabatic regime. We briefly discuss possible applications of the general theory to the problem of the qubit decoherence and to the spin relaxation of molecular magnets.