Non-classical properties of two-mode squeezed cross-Kerr state and its non-Gaussian character based on the cumulants

In this paper, our focus is to explore the generation of a two-mode “squeezed cross-Kerr state (SCKS)” and its non-classical properties. We have thoroughly studied SCKS’s many non-classical characteristics, which have revealed its unique non-classical characteristics, throughout our investigation. One of the primary properties that we examined is higher-order squeezing, which reveals the degree to which the SCKS surpasses the limits of classical states in terms of the squeezing phenomenon. This higher-order squeezing signifies the presence of non-classical behavior in the state, offering valuable insights into its quantum nature. In addition to this, we looked at the Pearson correlation coefficient, which can be used as a measure of the state’s non-classical correlations. It enables us to have a better understanding of the non-classical entanglement present in the two-mode SCKS and how it differs from classical correlations. Furthermore, we explored the phenomenon of anti-bunching, a remarkable feature of non-classical light where photons tend to avoid arriving at the same point in time. Our investigation allowed us to assess the degree of photon antibunching in the SCKS, providing essential information about the state’s departure from classical behavior. Furthermore, we have calculated cumulants, which are statistical measures used to quantify the non-classical nature of the state. We obtained useful insights into the higher-order statistical correlations of the two-mode SCKS by analyzing cumulants, allowing us to distinguish them from classical statistical distributions.