The photon blockade effects in a system consisting of an artificial giant atom coupled with three cavities are investigated. By solving the Schrödinger equation, we obtain the steady-state probability amplitudes of the system and derive the analytical expressions for the equal-time second-order correlation function. Based on these analytical expressions, the optimal conditions for achieving the photon blockade under different driving conditions are derived in detail.

We first examine the energy spectra and transition pathways for the single-photon and two-photon excitations in weakly driven cavity mode, and then investigate the statistical properties of photons. It is demonstrated that the optimal conventional photon blockade can be achieved by selecting appropriate driving detuning as characterized by the equal-time second-order correlation function of g^\left(2\right)\left(0\right)\approx10^-3.4 . Remarkably, we observe that both cavities of the system exhibit robust photon blockade effects against the weak driving. It is also found that with the increase of the coupling strength between the artificial giant atom and cavities, the photon blockade phenomenon becomes more pronounced while maintaining its robustness to the weak driving. Furthermore, we consider the case of simultaneously driving both the artificial giant atom and cavity modes. The unique multi-point coupling characteristics of the artificial giant atom provide additional transition pathways for photons, thereby allowing us to use the resulting quantum interference to further enhance photon blockade. When the system satisfies the optimal parametric conditions for both the conventional and unconventional photon blockade effects, one cavity exhibits exceptional photon blockade with g^\left(2\right)\left(0\right)\approx10^-6.5 .

This research greatly relaxes the stringent parameter requirements for the experimental realization of single-photon sources and provides a theoretical support for improving their quality, which is crucial for achieving high-performance single-photon sources.