Effects of a nonlinear bath at low temperatures

TL;DR

This paper investigates the effects of a nonlinear quantum bath at low temperatures using numerical flow-equation methods, focusing on a two-level system coupled to a nonlinear bath and comparing it to a linear bath.

Contribution

It derives flow equations for a four-level system coupled to an oscillator bath at low temperatures and applies this to analyze a two-level system with a nonlinear bath.

Findings

Differences between nonlinear and linear bath effects at low temperatures.

Validation of flow equations for a four-level system.

Insights into the relaxational dynamics of a spin in a nonlinear environment.

Abstract

We use the numerical flow-equation renormalization method to study a nonlinear bath at low temperatures. The model of our nonlinear bath consists of a single two-level system coupled to a linear oscillator bath. The effects of this nonlinear bath are analyzed by coupling it to a spin, whose relaxational dynamics under the action of the bath is studied by calculating spin-spin correlation functions. As a first result, we derive flow equations for a general four-level system coupled to an oscillator bath, valid at low temperatures. We then treat the two-level system coupled to our nonlinear bath as a special case of the dissipative four-level system. We compare the effects of the nonlinear bath with those obtained using an effective linear bath, and study the differences between the two cases at low temperatures.