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Chinese Physics Letters

Entanglement Swapping and Concentration in Multi-Pair Bose–Einstein Condensates

Cao Yong-zheng, Kuang Le-Man

Published Jan 30, 2006• 2 citations
Publisher

Abstract

We propose a scheme of entanglement swapping and concentration in a system consisting of multi-pair entangled trapped Bose–Einstein condensates (BECs). In this scheme, entanglement swapping is accomplished by using interference-pattern joint measurements and detecting the total number of condensed atoms leaking out of relevant traps while entanglement concentration is realized by controlling inter-atomic nonlinear and tunnelling interactions. Three- and four-pair BEC schemes are investigated in detail. It is found that with the increasing number of the entangled pairs, the region of entanglement concentration is broadened and the amount of concentrated entanglement is enhanced.

DOI
10.1088/0256-307x/23/2/002

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We propose a scheme of entanglement swapping and concentration in a system consisting of multi-pair entangled trapped Bose–Einstein condensates (BECs). In this scheme, entanglement swapping is accomplished by using interference-pattern joint measurements and detecting the total number of condensed atoms leaking out of relevant traps while entanglement concentration is realized by controlling inter-atomic nonlinear and tunnelling interactions. Three- and four-pair BEC schemes are investigated in detail. It is found that with the increasing number of the entangled pairs, the region of entanglement concentration is broadened and the amount of concentrated entanglement is enhanced.
我们建议纠纷在由多对组成的一个系统交换和集中的一个计划纠缠了套住的 Bose 爱因斯坦冷凝物(BEC ) 。在这个计划，纠纷交换被使用干扰模式关节大小并且检测当纠纷集中被控制内部原子的非线性、掘的相互作用认识到时，从相关陷井漏的压缩原子的全部的数字完成。三 -- 并且四个 pairBEC 计划详细被调查。与纠缠的对的增加的数字，纠纷集中的区域被拓宽，集中的纠纷的数量被提高，这被发现。
We present a scheme for generating entangled state in two-species Bose-Einstein Condensate(BEC)with tunneling coupling.It's shown that the entanglement is independent of the tunneling coupling;the best entanglement is independent of the interaction in two-species in the condensate and the interaction accelerates the atoms in the condensate into the entangled state.It's also shown that one may faster generating the better entangled state by increasing the number of atoms in the condensate.
Based on the interference effect of polarized photons, we propose a practical scheme for entanglement concentration of unknown atomic entangled states. In the scheme, two λλ-type atoms belonging to different entangled pairs are individually trapped in two spatially separated cavities. By the subsequent detection of the polarized photons leaking out of the separate optical cavities, Alice and Bob as two distant parties can probabilistically extract one maximally entangled four-atom Greenberger–Horne–Zeilinger (GHZ) state from two identical partially entangled Einstein–Podolsky–Rosen (EPR) pairs. We also discuss the influence of cavity decay on the success probability of the scheme. The scheme is feasible and within the reach of current experimental technology.
We determine the behaviour of entanglement between regions of space in a Bose gas of fixed particle number around the critical temperature condensation. Long-range correlations develop in the Bose-Einstein condensate (BEC) phase transition and the aim here is to find out whether spatial coherence alone implies entanglement. We use a purity measure of entanglement to derive an entanglement witness that detects entanglement between two regions of space in the BEC. It is shown that spatial coherence between the two regions is necessary for entanglement with coherence and entanglement becoming equivalent only when the regions occupy the entire confining volume of the gas. The probabilities for Bosons to occupy the regions is the only other parameter that influences the amount of entanglement. We calculate explicitly the amount of entanglement between two regions for a cigar-shaped harmonic potential and find that it increases with decreasing temperature. A second entanglement witness is derived for entanglement between three regions of space, where again spatial coherence between each pair of regions is precursor to entanglement. It is shown that the state with the maximum amount of entanglement occurs when the probabilities for the Bosons to occupy the three regions are equal.