Extended system-bath entanglement theorem for multiple bosonic or fermionic environments

TL;DR

This paper extends the system-bath entanglement theorem to include multiple bosonic and fermionic environments under field-dressed conditions, enabling better analysis of nonlinear spectroscopy and transport phenomena.

Contribution

The work generalizes the SBET to complex environments with optical properties and multiple temperatures, incorporating field effects and fermionic cases for the first time.

Findings

Extended SBET applicable to multiple bosonic environments at different temperatures.

Inclusion of environment optical polarizability in the theorem.

Application to nonlinear spectroscopy and transport scenarios.

Abstract

The system-bath entanglement theorem (SBET) was established in terms of linear response functions [J. Chem. Phys. 152, 034102 (2020)] and generalized to correlation functions [arXiv: 2312.13618 (2023)] in our previous works. This theorem connects the entangled system-bath properties to the local system and bare bath ones. In this work, firstly we extend the SBET to field-dressed conditions with multiple bosonic Gaussian environments at different temperatures. Not only the system but also environments are considered to be of optical polarizability, as in reality. With the aid of the extended SBET developed here, for the evaluation of the nonlinear spectroscopy such as the pump-probe, the entangled system-bath contributions can be obtained upon reduced system evolutions via certain quantum dissipative methods. The extended SBET in the field-free condition and its counterpart in the classical limit is also presented. The SBET for fermionic environments is elaborated within the transport scenarios for completeness.