Comment on "Solvability of the two-photon Rabi Hamiltonian"

TL;DR

This paper critiques a previous implicit formula for the two-photon Rabi model spectrum, showing that the functions used are identically zero, which invalidates the spectrum determination method proposed earlier.

Contribution

It clarifies that the previously proposed functions for spectrum calculation are identically zero, challenging the validity of the earlier method.

Findings

The functions $G_c(z, E)$ are identically zero.

The spectrum cannot be obtained from the roots of these functions.

The critique invalidates the previous spectrum formula.

Abstract

An implicit formula for the spectrum of the two-photon Rabi model was presented by Travenec in Phys. Rev. A 85, 043805 (2012) in analogy to the method of Braak [Phys. Rev. Lett. 107, 100401 (2011)]. The spectrum is given by common zeros of four functions $G_c(z, E)$ taken with a fixed value of $z\in\mathbb{C}$. We point out that all the $G_c(z,E)$ functions defined by Travenec are identically zero, thus the spectrum is not in fact given by their roots.