Nonreciprocal photon blockade induced by parametric amplification in an asymmetrical cavity

We propose a scheme to generate and manipulate nonreciprocal photon blockade effect in an asymmetrical Fabry-P\'erot cavity, which consists of a single two-level atom and a second-order nonlinear medium. By utilizing the intrinsic spatial asymmetry of cavity and applying a parametric amplification pumping laser to the nonlinear medium, we can realize direction-dependent single-photon and two-photon blockade effects. For nonreciprocal single-photon blockade, our proposal is robust across a wide range of parameters, such as the cavity or atomic detuning, coupling strength, and atomic decay. Within similar parameter ranges, nonreciprocal two-photon blockade can be achieved and modulated by finely adjusting the parametric amplification pumping. Our project offers a feasible access to generating high-quality and tunable nonreciprocal single- or two-photon sources and paves a new avenue for investigating the nonreciprocity of photon quantum statistical properties.