Two-level system coupled to a boson mode: the large n limit

Generalized Rabi models: Diagonalization in the spin subspace and differential operators of Dunkl type

“…It holds trivially that U jkl σ 0 U −1 jkl = σ 0 . Given the properties (16), one can verify that (modulo a sign change and multiplication by R):…”

“…(22). In the case of U 132 , one finds with the help of identities (16) parameter extension of the Rabi model which smoothly interpolates between the latter and the Jaynes-Cummings model, the so-called generalized Rabi model (GRM), and of the two-photon and the two-mode quantum Rabi models was shown to enable their diagonalization in the spin subspace. The demonstrated diagonalized representation is expected to greatly simplify the description of time evolution and dissipative dynamics of the models.…”

“…One has U F G = U −1 132 = U 13,−2 , where the minus sign in front of 2 stands for the inverse of U 2 in the definition (7). On combining relations (16),…”

“…ĤgR becomes a first-order differential operator on B ⊗ C 2 , where B is the Fock-Bargmann Hilbert space of entire analytic functions isomorphic to L 2 (R) [9]. The GRM interpolates between the Jaynes-Cummings model (JCM) [11] (for k 2 = 0) and the original quantum Rabi model (RM) [12][13][14][15][16][17][18][19][20][21][22] (for k 1 = k 2 = k). The RM describes the simplest interaction between a cavity mode with a bare frequency ω and a two-level system, or a qubit, with a bare resonance frequency ω 0 .…”

Oscillatory Behavior of Large Eigenvalues in Quantum Rabi Models

“…(1.5) 1.2.2. The large n behavior of λ n (J) was already investigated by Schmutz [16]. Let J 0 denote the operator defined by (1.3)-(1.2) when ρ = 0, i.e.,…”