Comment on “Solvability of the two-photon Rabi Hamiltonian”
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak · Physical Review A · 2015
An implicit formula for the spectrum of the two-photon Rabi model was presented by Trav\ifmmode \check{e}\else \v{e}\fi{}nec 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 $z\ensuremath{\in}\mathbb{C}$. We point out that all the ${G}_{c}(z,E)$ functions defined by Trav\ifmmode \check{e}\else \v{e}\fi{}nec are identically zero, thus the spectrum is not in fact given by their roots.