Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model
Anne Boutet de Monvel, Lech Zieliński
We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences ( E m + ) m = 0 ∞ , ( E m - ) m = 0 ∞ satisfying a three-term asymptotic formula with the remainder estimate O ( m - 1 ln m ) when m tends to infinity. By analogy to the one-photon quantum Rabi model, the leading three terms of this asymptotic formula, describe a generalized rotating-wave approximation for large eigenvalues of the two-photon quantum Rabi model.
Comptes Rendus Mathématique•Dec 21, 2023•0 citations