Quantum Entanglement in Superconducting Beamsplitters Henning Soller Capri

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 J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)

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. Schönenberger Phys. Rev. Lett. 107, 136801 J. Wei and V. Chandrasekhar Nature Physics 6, 494– 498 (2010)

How to detect?

Result:

for chosen axes m and m‘ Now let us consider just tunnel contacts: A. Di Lorenzo and Yu. V. Nazarov, Phys. Rev. Lett. 94, 210601, 2005

Nice in principle, but… • What happens for setups closer to actual experiments? • What about interaction effects? • Polarisation > 84 % is needed • Time-resolved detection scheme Other entanglement detection schemes: D. Loss and E. V. Sukhorukov, Phys. Rev. Lett. 84, 1035, 2000 G. Burkard, D. Loss, and E. V. Sukhorukov, Phys. Rev. B 61, R 16303, 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

Setups closer to experiment Chaotic cavity instead of tunnel contacts: J. P. Morten, D. Huertas-Hernando, W. Belzig, and A. Brataas, Europhys. Lett. 81, 40002, 2008 Result for the Bell parameter stays the same! Quantum dots instead of tunnel contacts: H. Soller and A. Komnik, Eur. Phys. J. D 63, 3, 2011 Result for the Bell parameter stays the same!

Interaction effects 1. Geometric suppression factors or usage of a topological insulator lead to length dependence of the nonlocal conductances Result for the Bell parameter stays the same! 2. Onsite interaction (phonons, Coulomb interaction, … ) Result for the Bell parameter stays the same!

Polarisation > 84 % needed Entanglement: The state of the system cannot be written as product state. Bell inequality: ε > 2 means that local reality is violated! Entanglement and Bell violation does not mean the same and generically it is easier to verify the presence of entanglement than the violation of local reality. S. M. Roy, Phys. Rev. Lett. 94, 010402, 2005 J. Uffink and M. Seevinck, Physics Letters A 372, 1205, 2008 If Alice‘s and Bob‘s measurement directions for spin are orthogonal we can prove that th maximal value for ε for a separable state is only √ 2 Only need ε > √ 2 to verify the presence of entanglement We only need polarisation P > 70% for an entanglement witness

Experimental Setup F 1 In. As G 1 QD 3 QD 4 QD 2 F 2 G 4 S F 4 G 3 F 3

measure nonlocal conductances directly eliminates the need for time-resolved measurement L. Hofstetter, S. Csonka, A. Baumgartner, G. Fülöp, S. d'Hollosy, J. Nygård and C. Schönenberger, Phys. Rev. Lett. 107, 136801, Kondo effect in superconductorferromagnet hybrids enhances the spin polarisation to ≈70% H. Soller, L. Hofstetter, S. Csonka, A. Levy Yeyati, C. Schönenberger and A. Komnik, in preparation Synthetic antiferromagnets allow for small switchable magnets C. Wang, Y. Cui, J. A. Katine, R. A. Buhrman and D. C. Ralph, Nat. Phys. 7, 496– 501, 2011

Conclusion • Scheme for Bell measurements • Theoretical Improvements • Experimental Realisation