Bell correlation of separated two-mode squeezed Bose-Einstein condensates

doi:10.3969/j.issn.1000-5641.2022.04.013

Abstract

Abstract:

In this paper, a method for testing the Bell correlation between two spatially separated two-mode squeezed Bose-Einstein condensates (BECs) is proposed. Using the referenced method, violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed. First, the method for producing the required physical states is introduced, and then the Bell correlation is tested by calculating the relevant factors using the normalized expected value of the particle number operator. It is shown that violation of the Bell inequality can be observed when $r \lesssim 0.49$ . One of biggest violations occurs, furthermore, when $r \to 0$ and $B = 2\sqrt 2 $ . The method is highly robust in the presence of noise.

Key words: spatially separated Bose-Einstein condensates, two-mode squeezed, Bell inequality

CLC Number:

O431.2

Xin MENG, Valentin IVANNIKOV, Tim BYRNES. Bell correlation of separated two-mode squeezed Bose-Einstein condensates[J]. Journal of East China Normal University(Natural Science), 2022, 2022(4): 131-138.

Figures/Tables 2

References 29

1	WANG X L, CHEN L K, LI W, et al. Experimental ten-photon entanglement. Physical Review Letters, 2016, 117 (21): 210502.
2	FRIIS N, MARTY O, MAIER C, et al. Observation of entangled states of a fully controlled 20-qubit system. Physical Review X, 2018, 8 (2): 021012.
3	EINSTEIN A, PODOLSKY B, ROSEN N. Can quantum-mechanical description of physical reality be considered complete?. Physical Review, 1935, 47, 777-780.
4	BELL J S. On the Einstein-Podolsky-Rosen paradox. Physics, 1964, 1 (3): 195- 200.
5	BRUNNER N, CAVALCANTI D, PIRONIO S, et al. Bell nonlocality. Reviews of Modern Physics, 2014, 86(2), 419- 478.
6	CLAUSER J F, HORNE M A, SHIMONY A, et al. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 1969, 23 (15): 880-884.
7	FREEDMAN S J, CLAUSER J F. Experimental test of local hidden-variable theories. Physical Review Letters, 1972, 28(14), 938- 941.
8	ASPECT A, DALIBARD J, ROGER G. Experimental test of Bell's inequalities using time-varying analyzers. Physical Review Letters, 1982, 49(25), 1804- 1807.
9	OU Z Y, MANDEL L. Violation of Bell’s inequality and classical probability in a two-photon correlation experiment. Physical Review Letters, 1988, 61(1), 50- 53.
10	MUNRO W J, REID M D. Violation of Bell’s inequality by macroscopic states generated via parametric down-conversion. Physical Review A, 1993, 47 (5): 4412-4421.
11	HORODECKI R, HORODECKI P, HORODECKI M, et al. Quantum entanglement. Reviews of Modern Physics, 2009, 81, 865- 942.
12	CHANG M S, HAMLEY C D, BARRETT M D, et al. Observation of spinor dynamics in optically trapped ⁸⁷Rb Bose-Einstein condensates . Physical Review Letters, 2004, 92(14), 140403.
13	KLEMPT C, GEBREYESUS G, SCHERER M, et al. Parametric amplification of vacuum fluctuations in a spinor condensate. Physical Review Letters, 2010, 104 (19): 195303.
14	PEISE J, KRUSE I, LANGE K, et al. Satisfying the Einstein-Podolsky-Rosen criterion with massive particles [J]. Nature Communications, 2015(6): 8984. DOI: 10.1038/ncomms9984.
15	LÜCKE B, SCHERER M, KRUSE J, et al. Twin matter waves for interferometry beyond the classical limit. Science, 2011, 334 (6057): 773- 776.
16	LANGE K, PEISE J, LÜCKE B, et al. Entanglement between two spatially separated atomic modes. Science, 2018, 360 (6387): 416- 418.
17	WALLS D F, MILBURN G J. Quantum Optics [M]. Berlin: Springer, 1994.
18	GERRY C, KNIGHT P. Introductory Quantum Optics [M]. Cambridge: Cambridge University Press, 2004.
19	CARMICHAEL H J. Statistical Methods in Quantum Optics 1 [M]. Berlin: Springer, 1999.
20	SCULLY M O, ZUBAIRY M S. Quantum Optics [M]. [S.l.]: American Association of Physics Teachers, 1999.
21	OUDOT E, BANCAL J-D, SCHMIED R, et al. Optimal entanglement witnesses in a split spin-squeezed Bose-Einstein condensate. Physical Review A, 2017, 95 (5): 052347.
22	JING Y, FADEL M, IVANNIKOV V, et al. Split spin-squeezed Bose-Einstein condensates. New Journal of Physics, 2019, 21 (9): 093038.
23	BYRNES T, ILO-OKEKE E O. Quantum atom optics: Theory and applications to quantum technology[EB/OL]. (2020-10-28)[2021-04-04]. https://doi.org/10.48550/arXiv.2007.14601.
24	PEZZÈ L, SMERZI A, OBERTHALER M K, et al. Quantum metrology with nonclassical states of atomic ensembles. Reviews of Modern Physics, 2018, 90(3), 035005.
25	BRAUNSTEIN S L, VAN LOOCK P. Quantum information with continuous variables. Reviews of Modern Physics, 2005, 77 (2): 513- 577.
26	RALPH T C, MUNRO W J, POLKINGHORNE R E S. Proposal for the measurement of Bell-type correlations from continuous variables. Physical Review Letters, 2000, 85(10), 2035- 2039.
27	KITZINGER J, CHAUDHARY M, KONDAPPAN M, et al. Two-axis two-spin squeezed states. Physical Review Research, 2020, 2(3), 033504.
28	MUNRO W J, REID M D. Violation of Bell’s inequality by macroscopic states generated via parametric down-conversion. Physical Review A, 1993, 47(5), 4412- 4421.
29	BARNETT S M, PHILLIPS L S, PEGG D T. Imperfect photodetection as projection onto mixed states. Optics Communications, 1998, 158 (1/2/3/4/5/6): 45- 49.

[1]	WANG Qiang, ZENG Jie, JIAO Gaofeng, YUAN Chunhua. Limit of multi-parameter phase estimation in an actively correlated Mach-Zehnder interferometer [J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 135-142.
[2]	Shuai GAO, Matthew PREST, Ebubechukwu O. ILO-OKEKE, Manikandan KONDAPPAN, Juan E. ARISTIZABAL-ZULUAGA, Valentin IVANNIKOV, Tim BYRNES. Optically mediated entanglement between Bose-Einstein condensates [J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 93-105.