Quantum Rabi–Stark model: solutions and exotic energy spectra

Abstract

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestingly, a first-order quantum phase transition indicated by level crossing of the ground state and the first excited state is induced by the positive nonlinear Starklike coupling, which is however absent in any previous isotropic quantum Rabi models. When the absolute value of the nonlinear coupling strength is equal to twice the cavity frequency, this model can be reduced to an effective quantum harmonic oscillator, and solutions are then obtained analytically. The spectra collapse phenomenon is observed at a critical coupling, while below this critical coupling, infinite discrete spectra accumulate into a finite energy from below.

Multiple photon antibunching-to-bunching transitions in the dissipative anisotropic quantum Rabi model

“…To demonstrate this point, we study the two-photon correlation function of the dissipative quantum Rabi-Stark model [66,67] in Appendix. Since there is only a single 1st-order QPT in this model [68], we really find two antibunching area. The pronounced bouncing peak in between the two antibunching areas also signifies the 1st-order QPT.…”

“…By simulating the QRM with resonant Raman transition in 87 Rb atom interacting with high finesse cavity model [66], a nonlinear coupling term U σ z a † a emerges, which is conceptually relevant to the dynamical Stark shift in quantum optics. There exist a single 1st-order QPT in the QRSM model when |U/ω 0 | < 1 [68].…”

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

“…A few typical models are listed in Table 1 . Besides introducing the asymmetry from the bias, [ 3 ] as inspired by experimental setups nonlinear terms can be also added to interplay with the linear coupling, such as the two‐photon process, [ 10–12,60–63 ] the Stark‐like coupling, [ 11,12,64,65 ] and the A 2 term. [ 33 ] As one knows, the reduced symmetry from the JCM to the QRM leads to avoided crossings, [ 8 ] while the nonlinearity and the bias results in various patterns of symmetry breaking, different orders of transitions and a rich physics of tricriticalities and quadruple points.…”

Bound states of two-photon Rabi model at the collapse point

“…At the collapse point = ω/2, the fourth order differential equations can be much simplified into second order differential equations similar to the work on Rabi-Stark model [31]. Then these equations can be handled more easily using the similarity to Schrodinger equation.…”

“…A research has been done on the Rabi-Stark model which is another generalization of QRM with Stark-like term [31]. A real space approach has been used to explain the spectral accumulation occurs at critical coupling.…”