Abstract
We investigate statistical aspects of the entanglement production for open chaotic mesoscopic billiards in contact with superconducting parts, known as Andreev billiards. The complete distributions of concurrence and entanglement of formation are obtained by using the Altland–Zirnbauer symmetry classes of circular ensembles of scattering matrices, which complements previous studies in chaotic universal billiards belonging to other classes of random matrix theory. Our results show a unique and very peculiar behavior: the realization of entanglement in a Andreev billiard always results in non-separable state, regardless of the time reversal symmetry. The analytical calculations are supported by a numerical Monte Carlo simulation.
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References
C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
P.A. Mello, N. Kumar, Quantum transport in mesoscopic systems: complexity and statistical fluctuations (Oxford University Press, New York, 2004)
T. Heinzel, Mesoscopic electronics in solid state nanostructures (Wiley-VCH Verlag GmbH Co. KGaA, Weinheim, 2007)
S. Gustavsson et al., Surf. Sci. Rep. 64, 191 (2009)
J.G.G.S. Ramos, D. Bazeia, M.S. Hussein, C.H. Lewenkopf, Phys. Rev. Lett. 107, 176807 (2011)
A.L.R. Barbosa, M.S. Hussein, J.G.G.S. Ramos, Phys. Rev. E 88, 010901(R) (2013)
B. Dietz, A. Richter, R. Samajda, Phys. Rev. E 92, 022904 (2015)
C.W.J. Beenakker, M. Kindermann, C.M. Marcus, A. Yacoby, in Fundamental problems of mesoscopic physics, NATO Science Series II, Vol. 154, edited by I.V. Lerner, B.L. Altshuler, Y. Gefen (Kluwer, Dordrecht, 2004)
M.L. Mehta, Random matrices (Academic, New York, 1991)
P. Jacquod, R.S. Whitney, J. Meair, M. Buttiker, Phys. Rev. B 86, 155118 (2012)
H.U. Baranger, P.A. Mello, Phys. Rev. Lett. 73, 142 (1994)
R.A. Jalabert, J.-L. t Pichard, C.W.J. Beenakker, Europhys. Lett. 27, 255 (1994)
M.S.M. Barros, A.J. Nascimento Junior, A.F. Macedo-Junior, J.G.G.S. Ramos, A.L.R. Barbosa, Phys. Rev. B 88, 245133 (2014)
A.F. Macedo Junior, A.M.S. Macêdo, Phys. Rev. B 77, 165313 (2008)
A.F. Macedo-Junior, A.M.S. Macêdo, Phys. Rev. B 66, 041307 (2002)
A.J. Nascimento Júnior, M.S.M. Barros, J.G.G.S. Ramos, A.L.R. Barbosa, Eur. Phys. J. B 89, 194 (2016)
J.P. Dahlhaus, B. Béri, C.W.J. Beenakker, Phys. Rev. B 82, 014586 (2010)
J.J. Sakurai, Modern quantum mechanics (Addison-Wesley Publishing Company, New York Dom Mills, Ontario, 1994)
G. Alber, T. Beth, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, A. Zeilinger, in Quantum information (Springer, Berlin, 2001), Vol. 173
V.A. Gopar, D. Frustaglia, Phys. Rev. B 77, 153403 (2008)
F.A.G. Almeida, A.M.C. Souza, Phys. Rev. B 82, 115422 (2010)
D. Villamaina, P. Vivo, Phys. Rev. B 88, 041301 (2013)
A. Jarosz, P. Vidal, E. Kanzieper, Phys. Rev. B 91, 180203 (2015)
S. Rodriguez-Perez, M. Novaes, Phys. Rev. B 85, 205414 (2012)
J.G.G.S. Ramos, I.M.L. da Silva, A.L.R. Barbosa, Phys. Rev. B 90, 245107 (2014)
A. Altland, M.R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)
S. Rodriguez-Perez, M. Novaes, Braz. J. Phys. 45, 532 (2015)
C.W.J. Beenakker, C. Emary, M. Kindermann, J.L. Van Velsen, Phys. Rev. Lett. 91, 147901 (2003)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)
N.W. Ashcrof, N.D. Mermim, Solid state physics (Saunders College Publishing, USA, 1976)
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
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Ramos, J.G.G.S., Macedo-Junior, A.F. & Barbosa, A.L.R. Entanglement distribution statistic in Andreev billiards. Eur. Phys. J. B 90, 232 (2017). https://doi.org/10.1140/epjb/e2017-80033-8
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DOI: https://doi.org/10.1140/epjb/e2017-80033-8