Statistical analysis of quantum trajectories in dissipative Landau-Zener model

TL;DR

This paper analyzes quantum jump statistics in a dissipative Landau-Zener model, exploring how different dissipation types, bath temperature, and coupling influence quantum trajectories during adiabatic and non-adiabatic evolutions.

Contribution

It introduces a detailed statistical analysis of quantum jumps in a dissipative Landau-Zener system considering two dissipation models and environmental factors, advancing understanding of open quantum system dynamics.

Findings

Jump statistics differ between adiabatic and non-adiabatic regimes.

Bath temperature and coupling strength significantly affect jump probabilities.

The type of dissipation influences the projection basis of quantum jumps.

Abstract

We present statistics of quantum jumps in the two-level system with landau-Zener Hamiltonian that undergoes a Markovian process. For the Landau-Zener model, which is successful in simulating adiabatic/non-adiabatic evolution and quantum annealing, we consider two types of dissipation. In the first one, the jump operators project states to the initial ground state and excited state of the Hamiltonian at $t\to -\infty$. In the second type, the jump operators project to the instantaneous eigenstates of the Hamiltonian. By the quantum trajectories approach, we present the probability of the number of jumps in adiabatic and non-adiabatic regimes for both models. Furthermore, we demonstrate the statistics of jumps in time intervals of the evolutions. Also, we show the role of bath temperature, coupling strength to the environment, and spin-coupling directions on the statistics of quantum jumps.