Entanglement of electromagnetic fields

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 2, 2003, Pages

  Van Enk, S J ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC FIELDS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; OPTICAL BEAM SPLITTERS; PHOTONS;

ENTANGLEMENT; QUANTUM NUMBERS; QUANTUM STATE;

QUANTUM THEORY;

EID: 0038641946     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. For a similar discussion of systems and mode for indistinguishable partices, see P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001)
2. Phys. Rev. A 65, 042101 (2002).
3. j=0.
4. B |Ψ<>Ψ|.
5. This includes the possibility to define propagating modes: modes that consist of different frequencies become effective time-dependent modes and may be used to describe pulsed fields, see K.J. Blow, R. Loudon, S.J. Phoenix, and T.J. Shepperd, Phys. Rev. A 42, 4102 (1990).
6. →, are invariant.
7. This might be as good a place as any other to note that in standard QED a mode near a dielectric surface (such as a beam splitter) consists of the triplet of incoming reflected, and transmitted (or evanescent) beams, as in C.K. Carniglia and L. Mandel, Phys. Rev. D 3, 280 (1970). It has, however, become a practice to consider these three beams as separate modes.
8. MATLAB's FMINSEARCH, using a Nelder-Mead simplex (direct search) method.
9. S.J. van Enk, e-print quant-ph/0206135, which is an older version of the present paper.
10. M. Genovese and C. Novero, e-print quant-ph/0107118.
11. A.E. Mair, A. Vazari, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
12. A. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
13. For a nice review on orbital angular momentum of light, see L. Allen, M.J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
14. L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, and J.P. Woerdman, Phys. Rev. A 45, 8185 (1992)
15. S.J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992)
16. M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J.P. Woerdman, ibid. 96, 123 (1993)
17. S.J. van Enk, ibid. 102, 59 (1993).
18. L. Allen, J. Courtial, and M.J. Padgett, Phys. Rev. E 60, 7497 (1999).
19. H.H. Arnaut and G.A. Barbosa, Phys. Rev. Lett. 85, 286 (2000)
20. see also the Comment by E.R. Eliel, S.M. Dutra, G. Nienhuis, and J.P. Woerdman, ibid. 86, 5208 (2001)
21. S. Franke-Arnold, S.M. Barnett, M.J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
22. J.C. Howell, A. Lamas-Linares, and D. Bouwmeester, Phys. Rev. Lett. 88, 030401 (2002).
23. There are at most nine terms in the Schmidt decomposition: the four photons can be distributed among the two pairs of modes in nine different ways There is one state with a distribution (0 4), two with (1 3), three with (2 2), two with (3 1), and one with (4 0).
24. R.J.C. Spreeuw, Found. Phys. 28, 361 (1998)
25. Phys. Rev. A 63, 062302 (2001).
26. A. Peres, P.F. Scudo, and D.R. Terno, Phys. Rev. Lett. 88, 230402 (2002).