  The NOON states are valuable quantum resources, which have a wide range of
applications in quantum communication, quantum metrology, and quantum
information processing. Here we propose a fast, concise and reliable protocol
for deterministically generating the NOON states of two resonators coupled to a
single $\triangle$-type superconducting qutrit. In particular, we derive the
effective Hamiltonians at the multi-photon resonances by virtue of the strong
counter-rotating interaction between the resonator modes and the qutrit. Based
on these crucial effective Hamiltonians, our protocol simplifies the previous
ones using the single-photon resonance and consequently reduces the number of
operations for state preparation. To test the robustness of this protocol, we
analyze the effects from both the decoherence including dissipation and
dephasing and the crosstalk of resonator modes on the state fidelity through a
Lindblad master equation in the eigenstates of the full Hamiltonian.
