By combining analytical solutions and numerical simulations, we investigate the control mechanism of photon blockade effects in a hybrid quantum system consisting of a Kerr-medium single-mode cavity coupled with an optical parametric amplifier (OPA).

To study photon blockade in the system, the dynamics are described by a master equation derived from the effective Hamiltonian, which considers single-mode cavity decay. In order to obtain analytical solutions under optimal photon blockade conditions, the quantum state of the system is expanded to the two-photon level based on the Fock state, and the steady-state probability amplitudes are derived by solving the Schrödinger equation, thereby yielding analytical expressions for the optimal photon blockade regime. The results demonstrate that photon blockade can be achieved in the system at appropriate parameters. Comparative analysis shows excellent agreement between the analytical results and numerical simulations of the equal-time second-order correlation function, validating both the correctness of the analytical solutions and the effectiveness of photon blockade in the system.

The numerical results show that the average photon number significantly increases under resonant conditions, providing theoretical support for optimizing single-photon source brightness, which is essential for achieving high-brightness single-photon sources.

Furthermore, variations in the driving phase can cause the optimal photon blockade region to shift in the two-dimensional parameter space of driving strength and OPA nonlinear coefficient, and even reverse the opening direction of the parabolic-shaped optimal blockade region. Both numerical and theoretical results confirm the regulatory effect of the driving phase on photon blockade.

Additionally, the influence of Kerr nonlinearity is examined. The results show that photon blockade persists robustly over a broad range of Kerr nonlinear strengths, exhibiting universal characteristics.

Physical mechanism analysis indicates that the photon blockade effect originates from destructive quantum interference between two photon transition pathways in the system under specific parameters, effectively suppressing two-photon excitation. Although Kerr nonlinearity modulates the energy levels of the system, it does not affect the quantum interference pathways, thus keeping the photon blocking effect stable over a wide parameter range.