We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state, and make a comparison with existing approximations and the exact solution. The results show that the variational expansion is a significant improvement over the existing approximations for the AQRM.

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.