Improved experimental scheme for the generation of pair coherent state in traveling-wave optical fields

Pair coherent state (PCS) is a two-mode non-Gaussian state recently generated within spatially confined superconducting cavities. Under typical conditions, it is unsuitable for performing global quantum missions in open space. Several methods have been proposed to generate this state with the capability to propagate unrestrictedly. However, these methods employed an excessive amount of unnecessary physical resources or relied on coherent displacement within the low regime. This paper presents a novel experimental approach to generate this state, specifically designed for facilitating long-distance quantum information processing and communication tasks. The method involves the utilization of two weak cross-Kerr nonlinear media, two balanced beam splitters, and an on/off photodetector. Furthermore, the input comprises three CSs with high amplitudes. These physical resources are potentially accessible within existing technology. The analysis of success probability and fidelity demonstrates that the PCS can be successfully generated with a high coherent parameter amplitude, even in scenarios where the photodetector efficiency is low, provided that the coherent amplitudes are sufficiently high.