Hierarchy of higher-order correlation functions and photonblockade in non-Gaussian pair coherent states

Abstract Recently, non-Gaussian operations on pair coherent states have been shown to significantly enhance various nonclassical properties, including linear entropy, Q -function, and fidelity. In the present work, we perform a systematic investigation of higher-order correlation functions (CFs) for different classes of non-Gaussian pair coherent states (NGPCSs). Such higher-order correlations are experimentally accessible and provide direct signatures of fundamental quantum phenomena, including photon antibunching, photon blockade (PB), the possibility of single photon source, and multiphoton suppression, which are crucial for quantum information and communication applications. By evaluating the normalized second-, third-, and fourth-order CFs, we analyze the emergence of higher-order antibunching and the possibility of the PB phenomenon as functions of the state parameter | ξ | and photon-operation parameters. All considered states satisfy the hierarchy g ( 4 ) ( 0 ) < g ( 3 ) ( 0 ) < g ( 2 ) ( 0 ) < 1 , and, for suitable parameter regimes, g ( n ) ( 0 ) → 0 , indicating strong suppression of multiphoton excitations and PB. A systematic analysis is provided for different classes of NGPCSs, e.g. photon-added-subtracted, photon-subtracted-added, photon-added-added, and photon-subtracted in two modes of pair coherent states. These observations are further supported by some statistical ratios of CFs, e.g. quality factors, multiphoton suppression ratios, and score. Our results establish non-Gaussian photon engineering as a powerful approach for tailoring multiphoton statistics and realizing controllable few-photon light sources. The engineered pair coherent states studied here thus provide promising platforms for applications in quantum communication, quantum information processing, and photonic quantum technologies.