The anti-Jaynes-Cummings model is solvable : quantum Rabi model in rotating and counter-rotating frames ; following the experiments

TL;DR

This paper demonstrates that the anti-Jaynes-Cummings component of the quantum Rabi model is exactly solvable, challenging the belief that it is intractable, and clarifies the model's dynamics in rotating and counter-rotating frames.

Contribution

It reveals the exact solvability of the anti-Jaynes-Cummings interaction within the quantum Rabi model, highlighting conserved excitation numbers and symmetries in different frames.

Findings

AJC interaction has a conserved excitation number operator

QRM dynamics include exactly solvable rotating and counter-rotating frames

The model clarifies the intractability misconception of AJC interaction

Abstract

This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC) interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specified by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counterrotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specified by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF.