Generalized squeezing rotating-wave approximation to the isotropic and anisotropic Rabi model in the ultrastrong-coupling regime

TL;DR

The paper introduces the generalized squeezing rotating-wave approximation (GSRWA), which employs displacement and squeezing transformations to better analyze the isotropic and anisotropic Rabi models in the ultrastrong-coupling regime, providing analytical expressions and improved accuracy.

Contribution

It develops the GSRWA method that incorporates squeezing effects, offering a more accurate analytical approach for the Rabi model in the ultrastrong-coupling regime compared to previous displacement-only methods.

Findings

Analytical expressions for mean photon number and ground-state energy with squeezing terms.

Significant improvement of GSRWA over previous methods in accuracy.

Validation of GSRWA effectiveness for both isotropic and anisotropic Rabi models.

Abstract

Generalized squeezing rotating-wave approximation (GSRWA) is proposed by employing both the displacement and the squeezing transformations. A solvable Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a qubit coupled to oscillators experiment, a well-defined Schr\"{o}dinger-cat-like entangled state is given by the displaced-squeezed oscillator state instead of the original displaced state. For the isotropic Rabi case, the mean photon number and the ground-state energy are expressed analytically with additional squeezing terms, exhibiting a substantial improvement of the GSRWA. And the ground-state energy in the anisotropic Rabi model confirms the effectiveness of the GSRWA. Due to the squeezing effect, the GSRWA improves the previous methods only with the displacement transformation in a wide range of coupling strengths even for large atom frequency.