  We study the ground states of the single- and two-qubit asymmetric Rabi
models, in which the qubit-oscillator coupling strengths for the
counterrotating-wave and corotating-wave interactions are unequal. We take the
transformation method to obtain the approximately analytical ground states for
both models and numerically verify its validity for a wide range of parameters
under the near-resonance condition. We find that the ground-state energy in
either the single- or two-qubit asymmetric Rabi model has an approximately
quadratic dependence on the coupling strengths stemming from different
contributions of the counterrotating-wave and corotating-wave interactions. For
both models, we show that the ground-state energy is mainly contributed by the
counterrotating-wave interaction. Interestingly, for the two-qubit asymmetric
Rabi model, we find that, with the increase of the coupling strength in the
counterrotating-wave or corotating-wave interaction, the two-qubit entanglement
first reaches its maximum then drops to zero. Furthermore, the maximum of the
two-qubit entanglement in the two-qubit asymmetric Rabi model can be much
larger than that in the two-qubit symmetric Rabi model.
