## 1 Introduction  
Single photon source and single photon detectors have great potential applications in precision measurement instruments, quantum information computing, and quantum communications [1; 2]. For instances, in quantum information science, single photons can be promising quantum bits on which information can be encoded using interferometers or polarization, and can be used in quantum key distribution and other applications. In other domains, single photon detectors are used in a wide range of applications, such as bioluminescence detection, Deoxyribonucleic acid (DNA) sequencing, and picosecond imaging circuit analysis. Single photon emitters deliver photons one at a time, which is also called photon antibunching phenomenon [3]. This single photon is quantized by its energy \(\dot{n}\
u_{k}\), where \(\hbar\) is [PERSON]'s constant, and \(\
u_{k}\) is the frequency of the \(k\)th mode in the quantized electromagnetic field. A single photon source can be generated by different mechanisms. [PERSON] [4] first generated single photons in 1974 based on a cascade transition of calcium atoms. [PERSON] and [PERSON] investigated the antibunching and sub-Poissonian properties of the resonance fluorescence of a single atomic ion stored in a radio-frequency trap [5]. Nano-objects in condensed matter are also possible sources of single photons [6], such as semiconductor nanocrystals [7], color centers in diamonds [8], and quantum dots [9; 10; 11]. In cavity quantum electrodynamics (QED), a photon blockade is typically achieved by the coupling of nonlinear freedoms that give rise to the anharmonicity of the Jaynes-Cummings ladder of the system eigenstates. A conventional photon blockade is the result of the strong nonlinearity of the system, which requires the single-photon nonlinearity to be at least larger than the mode linewidth \(\kappa\)[12; 13; 14; 15]. A photon blockade created in weakly nonlinear systems, which are far more natural in many areas of photonics and are more feasible to integration and scalability, is referred to as an unconventional photon blockade (UPB) [16; 17; 18]. The underlying mechanism for the UPB is the destructive quantum interference between different excitation pathways, which usually requires that the system involvesseveral degrees of freedom to establish multi-transition paths. The UPB was first put forward by [PERSON] and [PERSON] [16] in a pair of coupled quantum modes. The UPB has been, since then, studied in various cavity systems, such as two coupled Kerr nonlinear cavity structures with one laser-driven [19], one linear cavity coupled to a Kerr nonlinear cavity with one driving laser [20], two nonlinear cavities with two driving laser [21], two coupled Kerr cavities in a semiconductor [22] and in all-silicon [23], two overlapped cavities corresponding to low frequency and high frequency modes [24], and one cavity coupled to a quantum dot with two driving laser [25]. We know that physical mechanisms of conventional and unconventional photon blockades are different. For conventional photon blockades, the system needs to have a strong nonlinearity effect, whereas UPBs need a weak nonlinearity effect. For obtaining the unconventional photon blockade, we introduce a two-level atom system in Cavity B. We use a pump laser to couple the cavity field, and the interaction between the cavity and the atom can then be effectively manipulated, which provide a method for realization of the unconventional photon blockade. In this paper, we go back to the basic Jaynes-Cummings model and study the conventional and unconventional photon blockade effect in a linear cavity coupled to a nonlinear cavity. The nonlinearity of the second cavity is mediated by a two-level atom. An atom itself is a potential emitter of light, and the cavity can enhance the spontaneous emission rate and the photon production rate. The second cavity provides different transition paths for the photons in the first cavity.