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Quantum Entanglement in Superconducting Beamsplitters

Quantum Entanglement in Superconducting Beamsplitters. Henning Soller Capri, 16.4.2012. Definition of Entanglement. The state of the system cannot be written as a product state . spin states. ground state of BCS superconductor. R. F. Werner, Phys. Rev . A 40, 4277, 1989

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Quantum Entanglement in Superconducting Beamsplitters

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  1. Quantum Entanglement in SuperconductingBeamsplitters Henning Soller Capri, 16.4.2012

  2. Definition ofEntanglement The stateofthesystemcannotbewrittenas a productstate. spinstates groundstateof BCS superconductor R. F. Werner, Phys. Rev. A 40, 4277, 1989 J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108,1175 (1957)

  3. C. Schönenberger, Physik in unserer Zeit 2, 58-59, 2010 L. Hofstetter, S. Csonka, J. Nygard, and C. Schönenberger, Nature 461, 960, 2009 L. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk Phys. Rev. Lett. 104, 026801, 2010 L. Hofstetter, S. Csonka, A. Baumgartner, G. Fülöp, S. d’Hollosy, J. Nygård, and C. SchönenbergerPhys. Rev. Lett. 107, 136801, 2011 J. Wei and V. Chandrasekhar Nature Physics 6, 494–498 (2010)

  4. Howtodetect?

  5. Result: Result:

  6. forchosenaxesmandm‘ Nowletusconsider just tunnel contacts: A. Di Lorenzo and Yu. V. Nazarov, Phys. Rev. Lett. 94, 210601, 2005

  7. Nice in principle, but… • Whathappensforsetupsclosertoactualexperiments? • Whataboutinteractioneffects? • Polarisation > 84 % isneeded • Time-resolveddetectionscheme Other entanglementdetectionschemes: D. Loss and E. V. Sukhorukov, Phys. Rev. Lett. 84, 1035, 2000 G. Burkard, D. Loss, and E. V. Sukhorukov, Phys. Rev. B 61, R16303, 2000 N. M. Chtchelkatchev, G. Blatter, G. B. Lesovik, and T. Martin, Phys. Rev. B 66, 161320, 2002 A. Bednorz and W. Belzig, Phys. Rev. B 83, 125304, 2011

  8. Setups closertoexperiment Chaoticcavityinsteadof tunnel contacts: J. P. Morten, D. Huertas-Hernando, W. Belzig, and A. Brataas, Europhys. Lett. 81, 40002, 2008 Resultforthe Bell parameterstaysthe same! Quantum dotsinsteadof tunnel contacts: H. Soller andA. Komnik, Eur. Phys. J. D 63, 3, 2011 Resultforthe Bell parameterstaysthe same!

  9. Interaction effects 1. Geometricsuppressionfactorsorusageof a topologicalinsulatorleadtolengthdependenceofthenonlocalconductances Resultforthe Bell parameterstaysthe same! 2. Onsiteinteraction (phonons, Coulomb interaction,… ) Resultforthe Bell parameterstaysthe same!

  10. Polarisation > 84 % needed Entanglement: The stateofthesystemcannotbewrittenasproductstate. Bell inequality: ε > 2 meansthatlocalrealityisviolated! Entanglementand Bell violationdoes not meanthe same andgenerically itiseasiertoverifythepresenceofentanglementthantheviolationoflocalreality. S. M. Roy, Phys. Rev. Lett. 94, 010402, 2005 J. Uffink and M. Seevinck, Physics Letters A 372, 1205, 2008 IfAlice‘sandBob‘smeasurement directions for spin are orthogonal we can prove that the maximal value for εfor a separablestateisonly √2 Onlyneedε > √2 toverifythepresenceofentanglement Weonlyneedpolarisation P > 70% for an entanglementwitness

  11. Experimental Setup F1 G1 S G3 F3 QD 1 QD 3 InAs QD 4 QD 2 F2 G2 G4 F4

  12. measurenonlocalconductancesdirectly eliminatestheneedfor time-resolvedmeasurement L. Hofstetter, S. Csonka, A. Baumgartner, G. Fülöp, S. d'Hollosy, J. Nygårdand C. Schönenberger, Phys. Rev. Lett. 107, 136801, 2011 Kondo effect in superconductor-ferromagnethybridsenhancesthespinpolarisationto ≈70% H. Soller, L. Hofstetter, S. Csonka, A. Levy Yeyati, C. Schönenberger andA. Komnik, in preparation Syntheticantiferromagnetsallowforsmallswitchable magnets C. Wang, Y. Cui, J. A. Katine, R. A. Buhrmanand D. C. Ralph, Nat. Phys. 7, 496–501, 2011

  13. Conclusion

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