Geometric phase: an indicator of entanglement

S.N. Sandhya1, S. Banerjee2
1Department of Physics, Kanpur, India
2Department of Physics, Jodhpur, India

Tóm tắt

Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties of the two modes of radiation. The nonunitary, noncyclic path in the state space may be realized through the same control parameters which control the purity/mixedness and entanglement. We show analytically that the geometric phase is related to concurrence in certain region of the parameter space. We further show that the rate of change of the geometric phase reveals its resilience to fluctuations only for pure Bell type states. Lastly, the derivative of the geometric phase carries information on both purity/mixedness and entanglement/separability.

Tài liệu tham khảo

A. Shapere, F. Wilczek, Geometric Phases in Physics (World Scientific, Singapore, 1989) A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The Geometric Phase in Quantum Systems (Springer Verlag, Heidelberg, 2003) A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, J. Phys. A: Math. Theor. 43 (2010) (Special issue on Aharanov-Bohm effect and Geometric phase) E. Sjöqvist, Physics 1, 35 (2008) E. Knill, Nature 434, 39 (2005) L.-A. Wu, P. Zanardi, D.A. Lidar, Phys. Rev. Lett. 95, 130501 (2005) O. Oreshkov et al., Phys. Rev. Lett. 102, 070502 (2009) J.A. Jones, V. Vedral, A. Ekert, G. Castagnoli, Nature 403, 869 (2000) M.V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984) Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987) J. Anandan, Y. Aharonov, Phys. Rev. D 38, 1863 (1988) J. Samuel, R. Bhandari, Phys. Rev. Lett. 60, 2339 (1988) A.K. Pati, Phys. Rev. A 52, 2576 (1995) A.K. Pati, J. Phys. A: Math. Theor. 28, 2087 (1995) D.M. Tong, E. Sjöqvist, L.C. Kwek, C.H. Oh, Phys. Rev. Lett. 93, 080405 (2004) N. Mukunda, R. Simon, Ann. Phys. 228, 205 (1993) A. Carollo et al., Phys. Rev. Lett. 90, 160402 (2003) A. Carollo et al., Phys. Rev. Lett. 92, 020402 (2004) D.M. Tong et al., Phys. Rev. Lett. 93, 080405 (2004) K.-P. Marzlin et al., Phys. Rev. Lett. 93, 260402 (2004) M.S. Sarandy, D.A. Lidar, Phys. Rev. A 73, 062101 (2006) M.S. Sarandy et al., Phys. Rev. A 76, 052112 (2007) A. Uhlmann, Rep. Math. Phys. 24, 229 (1986) A. Uhlmann, Lett. Math. Phys. 21, 229 (1991) S. Banerjee, R. Srikanth, Eur. Phys. J. D 46, 335 (2008) E. Sjöqvist et al., Phys. Rev. Lett. 85, 2845 (2000) E. Sjöqvist, Phys. Rev. A 62, 022109 (2000) B. Hessmo, E. Sjöqvist, Phys. Rev. A 62, 062301 (2000) D.M. Tong et al., J. Phys. A: Math. Theor. 36, 1149 (2003) D.M. Tong et al., Phys. Rev. A 68, 022106 (2003) M. Ericsson et al., Phys. Rev. Lett. 91, 090405 (2003) P. Mehta, J. Samuel, S. Sinha, Phys. Rev. A 82, 034102 (2010) S.N. Sandhya, V. Ravishankar, Phys. Rev. A 82, 062301 (2010) J.G. Banacloche, Y.-Q. Li, S.-Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995) J.F. Clauser, Phys. Rev. D 9, 853 (1974) M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, 1997), p. 161 C.S. Castro, M.S. Sarandy, Phys. Rev. A 83, 042334 (2011)