Continuous Variable Entanglement and Violation of Bell Inequality for Two Modes in a Three-Level Cascade Atomic System

Yunxia Ping, Ze Cheng

Continuous variable entanglement and violation of Bell inequality for two modes are investigated in a three-level cascade atomic system. Entanglement of the system is demonstrated according to the entanglement criterion [Phys. Rev. Lett. 84 (2000) 2722]. Violation of Bell inequality is studied within the framework of a quantum theory of multiwave mixing. It is shown that there are some states that are entangled but do not violate the Bell inequality.

Yunxia Ping, Bo Zhang, Ze Cheng +1 more

Eyob Alebachew Sete

We investigate violation of Cauchy–Schwarz and Bell inequalities in two-mode three-level cascade system with injected atomic coherence in the framework of quantum theory of multiwave mixing. We show that Cauchy–Schwarz inequality is strongly violated when there is strong entanglement in the system. It also appears that Bell inequality is violated in the region where there is weak entanglement and well-preserved where there is strong entanglement in the system. We thus note that there are states which are entangled but do not violate Bell inequality. We also show that this system can be used to prepare states that exhibit EPR correlations.

Y. Ping, Bai-Yun Zhang, Z. Cheng

Yunxia Ping, Lie Liu, Chaomin Zhang +1 more

Violations of Bell inequality, Cauchy—Schwarz inequality and entanglement in a two-mode three-level atomic system are investigated. It is shown that there are some states, which are entangled but do not violate Bell inequality in this system. Moreover, the relations of violations of Bell inequality, Cauchy—Schwarz inequality, and entanglement are discussed in detail.

K. Berrada, S. Abdel‐Khalek