Publication: Experimental violation of a Bell-like inequality with optical vortex beams
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2015-11
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IOP Publishing
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Abstract
Optical beams with topological singularities have a Schmidt decomposition. Hence, they display features typically associated with bipartite quantum systems; in particular, these classical beams can exhibit entanglement. This classical entanglement can be quantified by a Bell inequality formulated in terms of Wigner functions. We experimentally demonstrate the violation of this inequality for Laguerre-Gauss (LG) beams and confirm that the violation increases with increasing orbital angular momentum. Our experimental scheme, which is designed to give directly the parity of the Wigner function, yields negativity at the origin for LG_10 beams, whereas for LG_20 we always get a positive value.
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©2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We acknowledge illuminating discussions with Gerd Leuchs, Elisabeth Giacobino, and Andrea Aiello. This work was supported by the Grant Agency of the Czech Republic (Grant 15-031945), the European Social Fund and the State Budget of the Czech Republic POSTUP II (Grant CZ.1.07/2.3.00/30.0041), the IGA of Palacky University (Grant PrF-2015-002), and the UCM-BSCH Program (Grant GR3/14).
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[1] Schrödinger E 1935 Math. Proc. Cambridge Philos. Soc 31 555–63.
[2] Einstein A, Podolsky B and Rosen N 1935 Phys. Rev. 47 777–80.
[3] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865–942.
[4] Bell J 1964 Physics 1 195–200.
[5] Clauser J F, Horne M A, Shimony A and Holt R A 1969 Phys. Rev. Lett. 23 880–4.
[6] Brunner N, Cavalcanti D, Pironio S, Scarani V and Wehner S 2014 Mod. Phys. Rev. 86 419–78.
[7] Werner R F and Wolf M M 2001 Quant. Inform. Compu. 1 1–25.
[8] Töppel F, Aiello A, Marquardt C, Giacobino E and Leuchs G 2014 New J. Phys. 16 073019.
IOPscience.
[9] Brunner N, Gisin N and Scarani V 2005 New J. Phys. 7 88.
IOPscience.
[10] Aiello A, Töppel F, Marquardt C, Giacobino E and Leuchs G 2015 New J. Phys. 17 043024.
IOPscience.
[11] Spreeuw R J C 1998 Found. Phys. 28 361–74.
[12] Ghose P and Mukherjee A 2014 Rev. Theor. Sci. 2 1–4.
[13] Hasegawa Y, Loidl R, Badurek G, Baron M and Rauch H 2003 Nature 425 45–8.
[14] Souza C E R, Huguenin J A O, Milman P and Khoury A Z 2007 Phys. Rev. Lett. 99 160401.
[15] Simon B N, Simon S, Gori F, Santarsiero M, Borghi R, Mukunda N and Simon R 2010 Phys. Rev. Lett. 104 023901.
[16] Borges C V S, Hor-Meyll M, Huguenin J A O and Khoury A Z 2010 Phys. Rev. A 82 033833.
[17] Qian X F and Eberly J H 2011 Opt. Lett. 36 4110–2.
[18] Gabriel C et al 2011 Phys. Rev. Lett. 106 060502.
[19] Qian X F, Little B, Howell J C and Eberly J H 2015 Optica 2 611–5.
[20] Pereira L J, Khoury A Z and Dechoum K 2014 Phys. Rev. A 90 053842.
[21] Fu J, Si Z, Tang S and Deng J 2004 Phys. Rev. A 70 042313.
[22] Lee K F and Thomas J E 2002 Phys. Rev. Lett. 88 097902.
[23] Goyal S K, Roux F S, Forbes A and Konrad T 2013 Phys. Rev. Lett. 110 263602.
[24] Chowdhury P, Majumdar A S and Agarwal G S 2013 Phys. Rev. A 88 013830.
[25] Kagalwala K H, Di Giuseppe G, Abouraddy A F and Saleh B E A 2013 Nat. Photon. 7 72–8.
[26] Karimi E, Boyd R W, de la Hoz P, de Guise H, Řeháček J, Hradil Z, Aiello A, Leuchs G and Sánchez-Soto L L 2014 Phys. Rev. A 89 063813.
[27] Beijersbergen M W, Allen L, van der Veen H and Woerdman J P 1993 Opt. Commun. 96 123–32.
[28] Peres A 1993 Quantum Theory: Concepts and Methods (Dordrecht: Kluwer).
[29] Stewart G W 1993 SIAM Rev. 35 551–66.
[30] Law C K, Walmsley I A and Eberly J H 2000 Phys. Rev. Lett. 84 5304–7.
[31] Agarwal G S and Banerji J 2002 Opt. Lett. 27 800–2.
[32] Sperling J and Vogel W 2011 Phys. Rev. A 83 042315.
[33] Banaszek K and Wódkiewicz K 1999 Phys. Rev. Lett. 82 2009–13.
[34] Ketterer A, Keller A, Coudreau T and Milman P 2015 Phys. Rev. A 91 012106.
[35] Borges C V S, Khoury A Z, Walborn S, Ribeiro P H S, Milman P and Keller A 2012 Phys. Rev. A 86 052107.
[36] Wigner E 1932 Phys. Rev. 40 749–59.
[37] Walther A 1968 J. Opt. Soc. Am. 58 1256–9.
[38] Bastiaans M J 2009 Phase-Space Optics: Fundamentals and Applications (New York: McGraw-Hill) 1–44 chap Wigner distribution in Optics.
[39] Galleani L and Cohen L 2002 Phys. Lett. A 302 149–55.
[40] Dragoman D 1997 The Wigner distribution function in optics and optoelectronics Progress in Optics vol 37 ed E Wolf (Amsterdam: Elsevier).
[41] Mecklenbraüker W and Hlawatsch F 1997 The Wigner Distribution: Theory and Applications in Signal Processing (Amsterdam: Elsevier).
[42] Alonso M A 2011 Adv. Opt. Photon. 3 272–365.
[43] Gisin N 1991 Phys. Lett. A 154 201–2.
[44] Simon R and Agarwal G S 2000 Opt. Lett. 25 1313–5.
[45] Zhang L, U’ren A B, Erdmann R, O’Donnell K A, Silberhorn C, Banaszek K and Walmsley I A 2007 J. Mod. Opt. 54 707–19.
[46] Mermin N D 1990 Phys. Rev. Lett. 65 1838–40.
[47] Royer A 1977 Phys. Rev. A 15 449–50.
[48] Mukamel E, Banaszek K, Walmsley I A and Dorrer C 2003 Opt. Lett. 28 1317–9.
[49] Smith B J, Killett B, Raymer M G, Walmsley I A and Banaszek K 2005 Opt. Lett. 30 3365–7.
[50] Schleich W 2000 Quantum Optics in Phase Space (Berlin: VCH-Wiley).
[51] Marchand E W and Wolf E 1974 J. Opt. Soc. Am. 64 1219–26.
[52] Prabhakar S, Reddy S G, Aadhi A, Perumangatt C, Samanta G K and Singh R P 2015 Phys. Rev. A 92 023822.
[53] Verbeeck J, Tian H and Schattschneider P 2010 Nature 467 301–4.
[54] McMorran B J, Agrawal A, Anderson I M, Herzing A A, Lezec H J, McClelland J J and Unguris J 2011 Science 331 192–5.
[55] D’Ambrosio V, Spagnolo N, Del Re L, Slussarenko S, Li Y, Kwek L C, Marrucci L, Walborn S P, Aolita L and Sciarrino F 2013 Nat. Commun. 4 2432.
[56] Töppel F, Aiello A, Marquardt C, Giacobino E and Leuchs G 2014 New J. Phys. 16 073019.
[57] Berg-Johansen S, Töppel F, Stiller B, Banzer P, Ornigotti M, Giacobino E, Leuchs G, Aiello A and Marquardt C 2015 Optica 2 864–8.
[58] D’Ambrosio V, Nagali E, Walborn S P, Aolita L, Slussarenko S and Marrucci L and Sciarrino F 2012 Nat. Commun. 3 961.
[59] Zhan Q and Leger J R 2002 Opt. Express 10 324–31.
[60] Dorn R, Quabis S and Leuchs G 2003 Phys. Rev. Lett. 91 233901.