Collective multipolelike signatures of entanglement in symmetric N -qubit systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 1, 2007, Pages

  Usha Devi, A R ^a   Prabhu, R ^a   Rajagopal, A K ^b,c  

^a BANGALORE UNIVERSITY   (India)

^b Krasnow Institute for Advanced Study   (United States)

^c Inspire Institute Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANGULAR MOMENTUM; ATOMS; CORRELATION METHODS; TENSORS;

BIPARTITE DIVISION; COGENT THEORY; ENTANGLEMENT; MULTIQUBIT STATES;

QUANTUM THEORY;

EID: 34547151176     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.012322     Document Type: Article

References (31)

1. J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1319 83, 1319 (1999)
2. A. Kuzmich, L. Mandel, and N. P. Bigelow, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1594 85, 1594 (2000).
3. D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.67 50, 67 (1994).
4. B. Yurke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1515 56, 1515 (1986)
5. M. Kitagawa and M. Ueda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1852 67, 1852 (1991)
6. V. Giovannetti, S. Lloyd, and L. Maccone, Science SCIEAS 0036-8075 10.1126/science.1104149 306, 1330 (2004)
7. C. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.150402 97, 150402 (2006).
8. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5932 81, 5932 (1998)
9. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature (London) NATUAS 0028-0836 10.1038/nature03064 432, 482 (2004)
10. J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, J. I. Cirac, and E. S. Polzik, Nature (London) NATUAS 0028-0836 10.1038/nature05136 443, 557 (2006).
11. K. G. H. Vollbrecht and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.062307 64, 062307 (2001)
12. H. P. Breuer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.062330 71, 062330 (2005)
13. H. P. Breuer, J. Phys. A JPHAC5 0305-4470 38, 9019 (2005)
14. D. Chruściński and A. Kossakowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062315 73, 062315 (2006).
15. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022112 67, 022112 (2003)
16. J. M. Geremia, J. K. Stockton, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042112 73, 042112 (2006).
17. M. Kitagawa and M. Ueda, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.5138 47, 5138 (1993).
18. A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London) NATUAS 0028-0836 10.1038/35051038 409, 63 (2001)
19. X. Wang and B. C. Sanders, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012101 68, 012101 (2003)
20. A. R. Usha Devi, M. S. Uma, R. Prabhu, and Sudha, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979206034406 20, 1917 (2006).
21. A. R. Usha Devi, M. S. Uma, R. Prabhu, and A. K. Rajagopal, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2006.11.073 364, 203 (2007).
22. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.120502 95, 120502 (2005)
23. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.259901 95, 259901 (E) (2005)
24. J. K. Korbicz, O. Guhne, M. Lewenstein, H. Haffner, C. F. Roos, and R. Blatt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.052319 74, 052319 (2006).
25. A. R. Usha Devi, R. Prabhu, and A. K. Rajagopal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.060501 98, 060501 (2007).
26. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
27. The spherical tensors τ QK are homogeneous polynomials of order K constructed from the angular momentum operators J as τ QK = NKJ (J) K YKQ (x,y,z), where YKQ (x,y,z) = rK YKQ (θ) are the solid harmonic functions. The choice of normalization factor NKJ = 2K K! 4π (2J-K) ! (2J+1) (2J+K+1) ! leads to their matrix elements in the { | JM } basis as given in the text. Note that the operators τ QK are related to the T KQ of Ref. through τ QK = [J] T KQ, so that τ 00 is a (2J+1) × (2J+1) identity matrix.
28. We mainly follow the notations and conventions of M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).
29. R. H. Dicke, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.93.99 93, 99 (1954).
30. K. Usami, J. I. Takahashi, and M. Kozuma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.043815 74, 043815 (2006).
31. B. Julsgaard, A. Kozhekin, and E. S. Polzik, Nature NATUAS 0028-0836 10.1038/35096524 413, 400 (2001).