  A novel, unexplored nonperturbative deep-strong coupling (npDSC) achieved in
superconducting circuits has been studied in the anisotropic Rabi model by the
generalized squeezing rotating-wave approximation (GSRWA). Energy levels are
evaluated analytically from the reformulated Hamiltonian and agree well with
numerical ones under a wide range of coupling strength. Such improvement
ascribes to deformation effects in the displaced-squeezed state presented by
the squeezed momentum variance, which are omitted in the previous displaced
state. The population dynamics confirm the validity of our approach for the
npDSC strength. Our approach paves a way to the exploration of analysis in
qubit-oscillator experiments for the npDSC strength by the displaced-squeezed
state.
