Method of spectral Green functions in driven open quantum dynamics

TL;DR

This paper introduces a spectral Green function method for simulating driven open quantum systems described by the Lindblad equation, simplifying calculations and enabling analysis of large many-body quantum systems.

Contribution

The paper develops a spectral Green function formalism that extends the Hilbert space approach, providing algebraic links between driven and non-driven dynamics in quantum systems.

Findings

Reduces computational cost significantly compared to full master equation solutions.

Enables study and optimization of large many-body quantum states.

Demonstrates effectiveness on a model of driven dissipative 2-level systems.

Abstract

A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space formalism and provides simple algebraic connections between the driven and non-driven dynamics in the spectral frequency domain. The formalism shows remarkable analogies to the use of Green functions in quantum field theory such as the elementary excitation energies and the Dyson self-energy equation. To demonstrate its potential, we apply the novel method to a coherently driven dissipative ensemble of 2-level systems comprising a single "active" subsystem interacting with $N$ "passive" subsystems -- a generic model with important applications in quantum optics and dynamic nuclear polarization. The novel method dramatically reduces computational cost compared with simulations based on solving the full master equation, thus making it possible to study and optimize many-body correlated states in the physically realistic limit of an arbitrarily large $N$.