The su(1,1)-like intensity-dependent Rabi model: A perturbative analysis of weak and strong-coupling regimes

Abstract

We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic¯eld and the two-level atom depends on the¯eld intensity. Upon modeling the matter-radiation coupling through the Holstein-Primako® realization of algebra suð1; 1Þ, we evaluate¯rst-and second-order eigenenergies and eigenstates both in the weakcoupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the¯rst case, among various e®ects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the suð1; 1Þ-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.

Delocalization effects, entanglement entropy and spectral collapse of boson mixtures in a double well

“…Hamiltonian (A.1) (emerging from the Bogoliubov approach and leading to the diagonal form (10)) thus predicts a spectral collapse of the energy levels for W 2 → U a U b . This mechanism is discussed in detail in [30] and [31]. The resulting macroscopic effect (also observed in Ref.…”

“…( 14), (N aR , N bL ) = (0, 0), ( levels for W 2 → U a U b . This mechanism is discussed in detail in [30] and [31]. The resulting macroscopic effect (also observed in Ref.…”

Continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

“…This is the case for nonlinear BH-like models but also for models describing matter-photon interactions whose nonlinearity is inherent in the spinor form of their Schrödinger problem. Several examples are known such as the transition to the super-radiant phase in the Dicke model, exhibiting the emergence of a quasicontinuous spectrum [26], and the interaction-induced spectral collapse characterizing the two-photon quantum Rabi model [27] in which the Hamiltonian becomes unitarily equivalent to a noncompact generator of su(1,1) [28].…”

Nonlinear Jaynes–Cummings model for two interacting two-level atoms

“…where the set of atomic states {| } f ñ k comes from having made use of a shorthand notation for the basis (8)- (10), namely, we have labeled…”

“…The JCM has become the source of inspiration for a wide variety of generalizations dealing with more general and/or realistic circumstances. The majority of them focused primarily upon multi-photon transitions and/or multimode fields [4][5][6]; engineering nonlinear atom-field couplings, like the Buck-Sukumar and Kochetov models [7,8] (including some very recent improvements and extensions of the former with or without applying the rotating wave approximation [9,10]), oneatom JC models involving two-photon interaction with intensity-dependence both in the atom-field coupling and the detuning [11,12], or adding nonlinear Kerr-like media [13][14][15][16]; interacting or noninteracting two two-level atoms [17][18][19][20]; or even more complex systems involving a large group of N twolevel (or multi-level) atoms in the same cavity, such as the socalled Tavis-Cummings model [21,22], to mention some examples. And still more recently, renewed attention has been paid to quantum decoherence and entanglement properties of light-matter interaction models à la Jaynes-Cummings whose central system is composed of two or three two-level atoms (also called within the jargon of the quantum information framework as two-or three-qubit systems) resonantly coupled with a cavity field prepared in a single number state and also with each other through dipole-dipole and Ising-like interactions [23,24] (incidentally, spin-spin interactions such as these or similar have also been the theme of current interest in a manifold of areas such as optical lattices [25]; systems with trapped ions [26] and microcavities [27]; and, even in the context of nearly localized and dipolarly coupled two identical molecules [28,29], where, under certain conditions, from an algebraic-structure point of view, intramolecular coupling models à la Jaynes-Cummings emerge); moreover, along this line an interesting application based on the resonant two-atom JCM has been proposed with the aim of implementing novel protocols for unambiguous Bell state discrimination for two qubits [30].…”