Violations of Bell Inequality,Cauchy-Schwarz Inequality andEntanglement in a Two-Mode Three-Level Atomic System

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.     

Observations of Bell Inequality Violations with Causal Isolation between Source and Detectors

We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH-S=2.30±0.07>2.00. This result rules out theories that explain correlations with traveling communication between source and detectors, including super-luminal and instantaneous communication.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

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

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.     

Production of Entanglement of Multiple Three-Level Atoms with a Two-Mode Cavity

A scheme is proposed for generating maximally entangled states for two or more three-level atoms. In the scheme the atoms are sent through a two-mode cavity one by one and interact with the two-cavity modes sequentially. The required experimental techniques are within the scope of what can be obtained in the microwave cavity QED setup.     

Inseparable Criterion and Bell Inequality

In this letter, we shall show how to construct constrained Bell-type inequality for a general two-party system, and violating this inequality is equivalent to being inseparable. For 2 × 2 system, the maximum violation is 3, while for 3 × 3 system, the largest violation is 11/3.     

The Essence of More Nonlocality with Less Entanglement in Bell Tests

In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more nonlocality with less entanglement. We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane. This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state. But the maximal Bell violation may not always happen on nonmaximally entangled state, because these probabilities will compete with each other, and the Bell violation behaves differently for various CH-type inequalities.     

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis-Cummings Model with Phase Decoherence

Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.     

Bell＇s Inequality for a System Composed of Particles with Different Spins

For two particles with different spins, we derive the Bell＇s inequality. The inequality is investigated for two systems combining spin-1 and spin-1/; spin-1/2 and spin-3/2. We show that for these states Bell＇s inequality is violated.     

Two-Photon Entanglement in a Two-Mode Supersymmetric Model

We will study entangled two-photon states generated from a two-mode supersymmetric model and quantify degree of entanglement in terms of the entropy of entanglement. The influences of the nonlinearity on the degree of entanglement is also examined, and it is shown that amount of entanglement increase with increasing the nonlinear coupling constant. PACS numbers: 03.67.-a, 03.67.Mn.     

Scheme for Robust Storage of Multi-particle Entanglement with a Cavity QED System

We propose a scheme for robustly storing multi-atom entangled states involving Bell states, three-particle W-state, n-particle W-like-states, generalized multi-particle W-states, n-particle GHZ-states, and partially entangled states in cavity QED. Our scheme can preserve the internal structure of the entangled states above, with only generation of a global phase corresponding to each of entangled states during the storage of them. One single-mode cavity and n identical two-level atoms are required. Our scheme may be realized in the present technology. The idea may be also utilized to store multi-trapped-ion entangled states in linear ion trap.     

Scheme for Robust Storage of Multi-particle Entanglement with a Cavity QED System

We propose a scheme for robustly storing multi-atom entangled states involving Bell states, three-particle W-state, n-particle W-like-states, generalized multi-particle W-states, n-particle GHZ-states, and partially entangled states in cavity QED. Our scheme can preserve the internal structure of the entangled states above, with only generation of a global phase corresponding to each of entangled states during the storage of them. One single-mode cavity and n identical two-level atoms are required. Our scheme may be realized in the present technology. The idea may be also utilized to store multi-trapped-ion entangled states in linear ion trap.     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665].In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.``     

Coherence-Enhanced Entanglement Induced by a Two-Mode Thermal Field

Considering two identical two-level atoms interacting with two mode thermal field through a nondegerate two-photon process, we study the entanglement dynamics between two atoms when the atomic coherence exists. It shows that the entanglement is dependent on the initial atomic states, and is greatly enhanced due to atomic coherence as compared with the case when the atomic coherence is ignored. The results also show that the entanglement can be controlled by changing the relative phases and the amplitudes of the polarized atoms.     

Coherence-Enhanced Entanglement Induced by a Two-Mode Thermal Field

Considering two identical two-level atoms interacting with two mode thermalfield through a nondegerate two-photon process, we study the entanglement dynamics between two atoms when the atomic coherence exists. It shows that the entanglement is dependent on the initial atomic states, and is greatlyenhanced due to atomic coherence as compared with the case when the atomic coherence is ignored. The results also show that the entanglement can be controlled by changing the relative phases and the amplitudes of the polarized atoms.     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665] .In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.