Quantum Entanglement in a Spin-Orbit Coupled Bose–Einstein Condensate**Supported by the Fundamental Research Funds for and the Central Universities under Grant No. F701108F01, the Natural Science Foundation of Anhui Province of China under Grant No. 1408085QA15, the Natural Science Foundation of Jiangsu Province of China under Grant Nos. BK20140128 and BK20140131, and the National Natural Science Foundation of Special Theoretical Physics

Abstract

We study the spin-field and the spin-spin entanglement in the ground state of a spin-orbit coupled Bose–Einstein condensate. It is found that the spin-field and the spin-spin entanglement can be induced by the spin-orbit coupling. By mapping the system to the Dicke-like model, the system exhibits a quantum phase transition from a normal (spin balanced) phase to superradiant (spin polarized) phase. The Dicke-like phase transition can be captured by the spin-field and the spin-spin entanglement arising from the spin-orbit coupling. The spin-field and the spin-spin entanglement increase as the Raman coupling increases in the superradiant phase, while they decrease with the Raman coupling increasing in the normal phase. We also consider the effect of a finite detuning on these entanglement show that the presence of the detuning suppresses the spin-field and the spin-spin entanglement.