Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study

TL;DR

This paper develops a concise analytical approach using adiabatic approximation and Bogoliubov operators to solve the generalized quantum Rabi model with one- and two-photon terms, revealing new phenomena and providing insights into Rabi oscillations and vacuum Rabi splitting.

Contribution

It introduces a novel adiabatic approximation method for the generalized quantum Rabi model with both couplings, offering analytical solutions and uncovering new physical phenomena.

Findings

Analytical eigenvalues and eigenstates obtained using adiabatic approximation.

Identification of two dominant Rabi frequencies in oscillations.

Discovery of new phenomena due to two-photon coupling term.

Abstract

A generalized quantum Rabi Hamiltonian with both one- and two-photon terms has emerged in the circuit quantum electrodynamics system for a decade. The usual parity symmetry is broken naturally in the simultaneous presence of both couplings, which complicates analytical treatments, even in the rotating wave approximations. In this paper, we propose an adiabatic approximation to this generic model by using Bogoliubov operators, and obtain a very concise analytical solution for both eigenvalues and eigenstates. Although the adiabatic approximation is only exact in the vanishing limit of the qubit frequency, the results for some physical observables nevertheless agree well with the numerical ones in a wide parameter regime. In the rotating-wave approximations, we also derive an analytical eigensolution. Two dominant Rabi frequencies are found in the Rabi oscillations of this generalized model. We also apply the present analytical theory to the vacuum Rabi splitting. It is found that some new phenomena emerge just because of the presence of the additional two-photon coupling term.