Geometric phase: an indicator of entanglement
The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics - Tập 66 - Trang 1-6 - 2012
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)