  An analytical variational method for the ground state of the biased quantum
Rabi model in the ultra-strong coupling regime is presented. This analytical
variational method can be obtained by a unitary transformation or alternatively
by assuming the form of ground state wave function. The key point of the method
is to introduce a variational parameter $\lambda$, which can be determined by
minimizing the energy functional. Using this method, we calculate physical
observables with high accuracy in comparison with the numerical exact one. Our
method evidently improves the results from the widely used general
rotating-wave approximation (GRWA) in both qualitative and quantitative ways.
