System-bath entanglement theorem with Gaussian environments

TL;DR

This paper introduces a theorem linking system-bath entanglement responses in Gaussian environments to local system responses, validated through exact methods, enabling enhanced analysis of quantum dissipation and entanglement properties.

Contribution

It establishes a novel system-bath entanglement theorem applicable to Gaussian environments, connecting total and local response functions, and broadening the scope of quantum dissipation theories.

Findings

The theorem is validated with exact dissipaton-equation-of-motion calculations.

Numerical demonstrations on Fano interference in spin-boson systems confirm the theorem's applicability.

The work enables evaluation of system-bath entanglement in existing quantum dissipation frameworks.

Abstract

In this work, we establish a so-called "system-bath entanglement theorem", for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local systems, as long as the interacting bath spectral densities are given. We validate the theorem with the direct evaluation via the exact dissipaton-equation-of-motion approach. Therefore, this work enables various quantum dissipation theories, which originally describe only the reduced system dynamics, for their evaluations on the system-bath entanglement properties. Numerical demonstrations are carried out on the Fano interference spectroscopies of spin-boson systems.