  The quantum Rabi model (QRM) describes the interaction between a two-level
system (qubit) and a quantum harmonic oscillator. In the limit where the qubit
frequency is smaller than the harmonic frequency, the QRM can be well
approximated by the adiabatic approximation (AA). The AA is widely used due to
its simplicity and explicit physical interpretation. However, the level
crossings in the spectrum of the QRM predicted by the AA are determined by the
zeros of Laguerre polynomials, which deviate from the exact points. We propose
a new approximation to the QRM that predicts the level crossings correctly.
This is done by exploiting a surprising connection between isolated exact
solutions to the QRM and the Laguerre polynomials in the AA. We thus refer to
this approach as the generalized adiabatic approximation (GAA). By
construction, the GAA always predicts the exact exceptional spectrum and
approximates the regular spectrum remarkably well in a much larger parameter
regime than the AA. This generalized approach offers a framework to deal with
the family of Rabi-type light-matter interaction models in a simple but
accurate manner.
