# Generalized coherent-squeezed-state expansion for the quantum Rabi model

## TL;DR

This paper introduces a variational method using coherent-squeezed states to accurately approximate the ground state of the quantum Rabi model, especially near phase transitions, outperforming previous coherent-state approaches.

## Contribution

The authors develop a systematic coherent-squeezed-state expansion that captures complex ground-state features and improves accuracy over traditional methods in the quantum Rabi model.

## Key findings

- Accurately reproduces ground-state energy and photon number in strong coupling regimes.
- Effectively describes the super-radiant phase with delocalized wave packets.
- Outperforms previous coherent-state methods near the critical regime.

## Abstract

We develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the coupling increases to form strong correlations physics in the vicinity of phase transition, we develop an improved wave function with a structure of two Gaussian wave packets, which is a linear superposition of two coherent-squeezed state. The ground-state energy and the average photon number agree well with numerical ones even in the strong-correlated regimes, exhibiting a substantial improvement over the coherent-state expansion. The advantage of the coherent-squeezed-state expansion lies in the inclusion of the second coherent-squeezed state and the additional squeezed deformation of the wave function, providing a useful tool for multi-modes spin-boson coupling systems of greater complexity.