Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System

TL;DR

This paper introduces a symmetric rotating wave approximation that accurately captures the behavior of the generalized single-mode spin-boson system in ultra and deep-strong coupling regimes, improving upon the traditional RWA.

Contribution

The authors develop a symmetric RWA that treats rotating and counter-rotating terms equally, preserving Hamiltonian invariances and extending applicability to strong coupling regimes.

Findings

The symmetric RWA reproduces qualitative features of the spectrum not captured by the original RWA.

It provides improved quantitative agreement with exact numerical results.

The method is extendable to higher accuracy and applicable to the two-photon Rabi Hamiltonian.

Abstract

The single-mode spin-boson model exhibits behavior not included in the rotating wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating wave approximation both off-resonance and at deep strong coupling. The symmetric rotating wave approximation allows for the treatment of certain ultra and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak coupling regime. Additionally, we symmetrize the generalized form of the rotating wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.