Generalized spin-squeezing inequalities in N -qubit systems: Theory and experiment

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 5, 2006, Pages

  Korbicz, J K ^a,b   Guhne O ^c   Lewenstein, M ^a,b   Haffner H ^c,d   Roos, C F ^c,d   Blatt, R ^c,d  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b INSTITUCIÓ CATALANA DE RECERCA I ESTUDIS AVANÇATS ICREA   (Spain)

^c ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^d UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTED PARAMETER NETWORKS; ELECTRON ENERGY LEVELS; IONS;

DICKE STATES; SPIN SQUEEZING PARAMETERS; SYMMETRIC STATES; TRIPARTITE ENTANGLEMENT;

QUANTUM THEORY;

EID: 33750993044     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.052319     Document Type: Article

References (49)

1. For pioneering experimental work, see 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. for very recent experiments on quantum feedback control, see J. M. Geremia, J. K. Stockton, and H. Mabuchi, Science SCIEAS 0036-8075 10.1126/science.1095374 304, 270 (2004);
3. for the recent review of spin squeezing using Gaussian states, see L. B. Madsen and K. Mølmer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70. 052324 70, 052324 (2004).
4. B. Julsgaard, A. Kohzekin, and E. S. Polzik, Nature (London) NATUAS 0028-0836 10.1038/35096524 413, 400 (2001).
5. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, Nature (London) NATUAS 0028-0836 10.1038/nature03064 432, 482 (2004).
6. L. Vaidman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.49.1473 49, 1473 (1994);
7. S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.869 80, 869 (1998).
8. D. M. Stamper-Kurn and W. Ketterle, Proceedings of Les Houches 1999 Summer School, Session LXXII (Springer, Berlin, 1999).
9. T.-L. Ho, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.742 81, 742 (1998).
10. T. Ohmi and K. Machida, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.1822 67, 1822 (1998);
11. T. Isoshima, K. Machida, and T. Ohmi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.4857 60, 4857 (1999).
12. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, Nature (London) NATUAS 0028-0836 10.1038/24567 396, 345 (1998).
13. For strongly correlated states of spin F=1 and F=2 atoms in optical lattices see M. Ueda and M. Koashi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.063602 65, 063602 (2002);
14. E. Demler and F. Zhou Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.163001 88, 163001 (2002);
15. A. Imambekov, M. Lukin, and E. Demler Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.063602 68, 063602 (2003).
16. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and I. C. Monroe, Nature (London) NATUAS 0028-0836 10.1038/35005011 404, 256 (2000);
17. D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, Science SCIEAS 0036-8075 10.1126/science.1097576 304, 1476 (2004).
18. C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Science SCIEAS 0036-8075 10.1126/science.1097522 304, 1478 (2004).
19. It is worth mentioning that using parametric down conversion it is possible to generate various entangled 3- and 4-photon states; see, for instance, M. Bourennane, M. Eibl, Ch. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, Ph. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087902 92, 087902 (2004);
20. M. Bourennane, M. Eibl, S. Gärtner, Ch. Kurtsiefer, H. Weinfurter, A. Cabello, O. Gühne, Ph. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, Int. J. Quantum Inf. ZZZZZZ 0219-7499 2, 133 (2004), and references therein.
21. C. F. Roos, G. P. T. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.220402 92, 220402 (2004);
22. H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, Nature (London) NATUAS 0028-0836 10.1038/nature04279 438, 643 (2005).
23. D. Leibfried, E. Knill, S. Seidelin, J. Britton, R. B. Blakestad, J. Chiaverini, D. B. Hume, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, R. Reichle, and D. J. Wineland, Nature (London) NATUAS 0028-0836 10.1038/nature04251 438, 639 (2005).
24. The Physics of Quantun Information, edited by, D. Bouwmeester, A. Ekert, and, A. Zeilinger, (Springer, New York, 2000);
25. M. Lewenstein, D. Bruß, J. I. Cirac, B. Kraus, M. Kus, J. Samsonowicz, A. Sanpera, and R. Tarrach, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400100014767 47, 2481 (2000).
26. M. Kitagawa and M. Ueda, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.5138 47, 5138 (1993).
27. A. Sørensen, L. M. Duan, J. I. Cirac, and P. Zoller, Nature (London) NATUAS 0028-0836 10.1038/35051038 409, 63 (2001).
28. X. Wang and B. C. Sanders, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012101 68, 012101 (2003).
29. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.120502 95, 120502 (2005);
30. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.259901 95, 259901 (E) (2005).
31. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996);
32. B. M. Terhal, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00401- 1 271, 319 (2000);
33. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.052310 62, 052310 (2000).
34. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
35. K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2002.6268 299, 88 (2002).
36. R. H. Dicke, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.93.99 93, 99 (1954).
37. F. Schmidt-Kaler, H. Häffner, S. Gulde, M. Riebe, G. P. T. Lancaster, T. Deuschle, C. Becher, W. Hänsel, J. Eschner, C. F. Roos, and R. Blatt, Appl. Phys. B: Lasers Opt. APBOEM 0946-2171 10.1007/s00340-003-1346-9 77, 789 (2003).
38. G. Tóth, C. Simon, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062310 68, 062310 (2003);
39. G. Tóth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052327 69, 052327 (2004);
40. G. Tóth, e-print quant-ph/0511237.
41. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
42. H. Häffner, F. Schmidt-Kaler, W. Hänsel, C. F. Roos, T. Körber, M. Chwalla, M. Riebe, J. Benhelm, U. D. Rapol, C. Becher, and R. Blatt, Appl. Phys. B: Lasers Opt. APBOEM 0946-2171 81, 151 (2005).
43. C. F. Roos, G. P. T. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.220402 92, 220402 (2004).
44. M. Ježek, J. Fiurášek, and Z. Hradil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012305 68, 012305 (2003);
45. Z. Hradil, J. Reháček, J. Fiurኡek, and M. Ježek, Lect. Notes Phys. LNPHA4 0075-8450 649, 59 (2004).
46. M. Reimpell (unpublished).
47. M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt-Kaler, D. F. V. James, and R. Blatt, Nature (London) NATUAS 0028-0836 10.1038/nature02570 429, 734 (2004).
48. A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.040401 87, 040401 (2001).
49. T.-C. Wei and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.042307 68, 042307 (2003).