Generalized adiabatic approximation to the asymmetric quantum Rabi model: conical intersections and geometric phases

The asymmetric quantum Rabi model (AQRM), which describes the interaction between a quantum harmonic oscillator and a biased qubit, arises naturally in circuit quantum electrodynamic circuits and devices. The existence of hidden symmetry in the AQRM leads to a rich energy landscape of conical intersections (CIs) and thus to interesting topological properties. However, current approximations to the AQRM fail to reproduce these CIs correctly. To overcome these limitations we propose a generalized adiabatic approximation (GAA) to describe the energy spectrum of the AQRM. This is achieved by combining the perturbative adiabatic approximation and the exact exceptional solutions to the AQRM. The GAA provides substantial improvement to the existing approaches and pushes the limit of the perturbative treatment into non-perturbative regimes. As a preliminary example of the application of the GAA we calculate the geometric phases around CIs associated with the AQRM.