One-Mode Wigner Quasi-probability Distribution Function for Entangled Coherent States Generated by Beam Splitter and Cavity QED

In this paper, we use the displacement operator together with parity operation to construct the superposition of two coherent states. By transmitting this superposition from 50-50 beam splitter the two-mode qubit like ECS is generated. Moreover, we introduce a controllable method for producing qutrit like ECS using atom-field interaction in cavity QED and beam splitter. We will show that the distances of peaks of Wigner functions for reduced density matrices of two-mode ECS's are entanglement sensitive and can be a witness for entanglement. To confirm the results we use concurrence measure to compare bipartite entanglement of ECS's with the behavior of peaks of Wigner functions. Moreover, we investigate decoherence effects on Wigner function, arising from transmitting ECS's through noisy channels.