Non-Markovian Quantum State Diffusion in a Fermionic Bath

TL;DR

This paper introduces a stochastic method for modeling the quantum dynamics of open systems in a fermionic environment, enabling probabilistic simulations of non-Markovian behavior using dressed quantum trajectories.

Contribution

It develops an exact fermionic quantum state diffusion approach that allows Monte-Carlo simulations of non-Markovian quantum dynamics in fermionic baths.

Findings

Provides a probabilistic framework for fermionic environments.

Enables long-time non-Markovian quantum simulations.

Shares properties with bosonic quantum state diffusion methods.

Abstract

We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these fluctuations in the basis of the particle-hole coherent states, then these fluctuations produce a classical particle-hole noise.The probability distribution of this noise is provided by the generalized particle-hole Husimi function of the vacuum. Then we define the dressed quantum trajectory as the evolution of the open system and the bath which is conditioned on a particular particle-hole noise sample. The resulting description resembles the non-Markovian quantum state diffusion for the bosonic bath. Therefore, we expect that our fermionic approach will share its favourable propeties like the possibility to carry out Monte-Carlo simulations of non-Markovian quantum dynamics on long times.