# An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

## TL;DR

This paper introduces an analytical variational approach to accurately determine the ground state of the biased quantum Rabi model in the ultra-strong coupling regime, surpassing the accuracy of traditional approximations.

## Contribution

The paper presents a novel variational method for the biased quantum Rabi model that improves accuracy over existing approximations in the ultra-strong coupling regime.

## Key findings

- High-accuracy calculation of physical observables
- Significant improvement over the general rotating-wave approximation
- Method applicable via unitary transformation or wave function assumption

## Abstract

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of ground state wave function. The key point of the method is to introduce a variational parameter $\lambda$, which can be determined by minimizing the energy functional. Using this method, we calculate physical observables with high accuracy in comparison with the numerical exact one. Our method evidently improves the results from the widely used general rotating-wave approximation (GRWA) in both qualitative and quantitative ways.