Analytical solutions to asymmetric two-photon quantum Rabi model and its exceptional spectrum

Abstract

Within the Segal-Bargmann representation, a generalized Rabi model is considered that includes both two-photon and asymmetric (bias) terms. It is shown that, through a suitable transformation, exact solutions can be obtained using the Bethe ansatz approach. Applying this approach to the meromorphic structure of the resulting fourth-order differential equation, arbitrary-state analytical solutions of the problem are presented for restricted values of parameters. Thereby, the exceptional spectrum of the qubit system is obtained. These exceptional points in the spectrum are of great experimental importance and directly associated with enhanced sensitivity and nontrivial dynamical behavior of the system since in the vicinity of these special parameter values, eigenstates become highly structured, making observables extremely sensitive to small changes in coupling or bias, an important feature for precise quantum control.