Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach

TL;DR

This paper introduces an exact quantum trajectory method for analyzing the non-Markovian dynamics of a three-level quantum system, enabling precise exploration of complex quantum behaviors without approximations.

Contribution

It presents the first exact, time-local quantum state diffusion equation for a three-level system in a non-Markovian environment, avoiding Markovian assumptions.

Findings

Established a convolutionless stochastic Schrödinger equation for the system

Provided a new tool for studying higher-dimensional quantum systems

Enabled exact analysis of non-Markovian quantum dynamics

Abstract

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr\"{o}dinger equation called time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.