Universality in dissipative Landau-Zener transitions

TL;DR

This paper develops an exact, non-perturbative method to analyze dissipative two-state quantum systems, revealing universal decay behavior in Landau-Zener transitions influenced by environmental noise.

Contribution

It introduces a novel random variable approach based on functional integrals for studying time-dependent dissipative quantum dynamics.

Findings

Universal decay of the upper state population at intermediate times

Method applicable at zero and finite temperatures

Potential implementation in cold-atom experiments

Abstract

We introduce a random variable approach to investigate the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of the time evolution of a quantum state vector subject to a Hamiltonian containing random noise fields. This numerically exact, non-perturbative formalism is particularly well suited in the context of time-dependent Hamiltonians, both at zero and finite temperature. As an important example, we consider the renowned Landau-Zener problem in the presence of an Ohmic environment with a large cutoff frequency at finite temperature. We investigate the 'scaling' limit of the problem at intermediate times, where the decay of the upper spin state population is universal. Such a dissipative situation may be implemented using a cold-atom bosonic setup.