  Anisotropic quantum Rabi model is a generalization of quantum Rabi model,
which allows its rotating and counter-rotating terms to have two different
coupling constants. It provides us with a fundamental model to understand
various physical features concerning quantum optics, solid-state physics, and
mesoscopic physics. In this paper, we propose an experimental feasible scheme
to implement anisotropic quantum Rabi model in a circuit quantum
electrodynamics system via periodic frequency modulation. An effective
Hamiltonian describing the tunable anisotropic quantum Rabi model can be
derived from a qubit-resonator coupling system modulated by two periodic
driving fields. All effective parameters of the simulated system can be
adjusted by tuning the initial phases, the frequencies and the amplitudes of
the driving fields. We show that the periodic driving is able to drive a
coupled system in dispersive regime to ultrastrong coupling regime, and even
deep-strong coupling regime. The derived effective Hamiltonian allows us to
obtain pure rotating term and counter-rotating term. Numerical simulation shows
that such effective Hamiltonian is valid in ultrastrong coupling regime, and
stronger coupling regime. Moreover, our scheme can be generalized to the
multi-qubit case. We also give some applications of the simulated system to the
Schr\"{o}dinger cat states and quantum gate generalization. The presented
proposal will pave a way to further study the stronger anisotropic Rabi model
whose coupling strength is far away from ultrastrong coupling and deep-strong
coupling regimes in quantum optics.
