Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 1, 2010, Pages

  Miranowicz, Adam ^a,b   Bartkowiak, Monika ^b   Wang, Xiaoguang ^a,c   Liu, Yu Xi ^a,d   Nori, Franco ^a,e  

^a RIKEN   (Japan)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

^c ZHEJIANG UNIVERSITY   (China)

^d TSINGHUA UNIVERSITY   (China)

^e UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOSONIC FIELDS; BOSONIC SYSTEMS; CAUCHY-SCHWARZ INEQUALITY; CREATION AND ANNIHILATION; EXPECTATION VALUES; MULTI-MODE FIELDS; MULTIMODES; NONCLASSICAL FIELDS; NONCLASSICALITY; P-FUNCTION; PHOTON ANTIBUNCHING; PHOTON-NUMBER CORRELATIONS; POLYNOMIAL FUNCTIONS; QUADRATURE SQUEEZING; SCHWARZ; SINGLE MODE;

PHOTONS;

QUANTUM ENTANGLEMENT;

EID: 77954940147     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.013824     Document Type: Article

References (93)

1. R. J. Glauber, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.131.2766 131, 2766 (1963).
2. E. C. G. Sudarshan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.10.277 10, 277 (1963).
3. V. V. Dodonov, and, V. I. Man'ko, (eds.), Theory of Nonclassical States of Light (Taylor & Francis, New York, 2003).
4. W. Vogel and D.-G. Welsch, Quantum Optics (Wiley-VCH, Weinheim, 2006).
5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
6. J. Peřina, Quantum Statistics of Linear and Nonlinear Optical Phenomena (Reidel, Dortrecht, 1991).
7. D. F. Walls, Nature NATUAS 0028-0836 10.1038/280451a0 280, 451 (1979).
8. R. Loudon, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/43/7/002 43, 913 (1980).
9. R. Loudon and P. L. Knight, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500348714550721 34, 709 (1987).
10. D. F. Smirnov and A. S. Troshin, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1987v030n10ABEH002966 30, 851 (1987)
11. D. F. Smirnov and A. S. Troshin, [Usp. Fiz. Nauk. 153, 233 (1987)].
12. D. N. Klyshko, Usp. Fiz. Nauk UFNAAG 0042-1294 10.3367/UFNr.0166.199606b. 0613 166, 613 (1996)
13. D. N. Klyshko, [Sov. Phys. Usp. 39, 573 (1996)].
14. V. V. Dodonov, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/4/1/201 4, R1 (2002).
15. X. Hu and F. Nori, Physica B PHYBE3 0921-4526 10.1016/S0921-4526(98) 01483-5 263, 16 (1999);
16. S. N. Shevchenko, A. N. Omelyanchouk, A. M. Zagoskin, S. Savel'ev, and F. Nori, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/7/073026 10, 073026 (2008);
17. A. M. Zagoskin, E. Il'ichev, M. W. McCutcheon, J. F. Young, and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.253602 101, 253602 (2008);
18. N. Lambert, C. Emary, Y. N. Chen, and F. Nori, e-print arXiv: 1002.3020.
19. K. C. Schwab and M. L. Roukes, Phys. Today PHTOAD 0031-9228 10.1063/1.2012461 58 (7), 36 (2005).
20. L. F. Wei, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.237201 97, 237201 (2006);
21. N. Lambert and F. Nori, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.214302 78, 214302 (2008).
22. G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, Nature (London) NATUAS 0028-0836 10.1038/nature05678 446, 782 (2007).
23. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
24. Th. Richter and W. Vogel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.283601 89, 283601 (2002).
25. A. Rivas and A. Luis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79. 042105 79, 042105 (2009).
26. G. S. Agarwal and K. Tara, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.485 46, 485 (1992).
27. E. Shchukin, Th. Richter, and W. Vogel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.011802 71, 011802 (R) (2005).
28. E. V. Shchukin and W. Vogel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.043808 72, 043808 (2005).
29. E. Shchukin and W. Vogel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.200403 96, 200403 (2006).
30. W. Vogel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100. 013605 100, 013605 (2008).
31. H. P. Yuen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.13.2226 13, 2226 (1976).
32. M. Kozierowski and R. Tanaś, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(77)90269-3 21, 229 (1977).
33. C. M. Caves and B. L. Schumaker, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.31.3068 31, 3068 (1985).
34. M. D. Reid and D. F. Walls, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.34.1260 34, 1260 (1986).
35. B. J. Dalton, Phys. Scr., T PHSTBO 0031-8949 10.1088/0031-8949/1986/T12/ 006 12, 43 (1986).
36. W. Schleich and J. A. Wheeler, Nature (London) NATUAS 0028-0836 10.1038/326574a0 326, 574 (1987).
37. G. S. Agarwal, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.5.001940 5, 1940 (1988).
38. A. Lukš, V. Peřinová, and J. Peřina, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(88)90322-7 67, 149 (1988);
39. A. Lukš, V. Peřinová, and Z. Hradil, Acta Phys. Pol. A 74, 713 (1988).
40. M. Hillery, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.3147 40, 3147 (1989).
41. C. T. Lee, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.1569 41, 1569 (1990);
42. C. T. Lee, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.1608 42, 1608 (1990).
43. X. T. Zou and L. Mandel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.475 41, 475 (1990).
44. D. N. Klyshko, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00091- 6 213, 7 (1996).
45. A. Miranowicz, J. Bajer, H. Matsueda, M. R. B. Wahiddin, and R. Tanaś, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/1/5/302 1, 511 (1999).
46. A. Miranowicz, H. Matsueda, J. Bajer, M. R. B. Wahiddin, and R. Tanaś, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/1/5/318 1, 603 (1999).
47. N. B. An and V. Tinh, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375- 9601(99)00602-7 261, 34 (1999).
48. N. B. An and V. Tinh, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375- 9601(00)00292-9 270, 27 (2000).
49. M. Jakob, Y. Abranyos, and J. A. Bergou, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/3/3/310 3, 130 (2001).
50. J. F. Clauser, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.9.853 9, 853 (1974).
51. H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.39.691 39, 691 (1977).
52. R. Short and L. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.51.384 51, 384 (1983).
53. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.2409 55, 2409 (1985).
54. P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/1/4/004 1, 173 (1986).
55. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.2044 59, 2044 (1987).
56. A. I. Lvovsky and J. H. Shapiro, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.033830 65, 033830 (2002).
57. M. Hillery, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.725 35, 725 (1987).
58. C. T. Lee, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.6586 45, 6586 (1992).
59. N. Lütkenhaus and S. M. Barnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.3340 51, 3340 (1995).
60. V. V. Dodonov, O. V. Man'ko, V. I. Man'ko, and A. Wünsche, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340008233385 47, 633 (2000).
61. P. Marian, T. A. Marian, and H. Scutaru, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.153601 88, 153601 (2002);
62. P. Marian, T. A. Marian, and H. Scutaru, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022104 69, 022104 (2004).
63. V. V. Dodonov and M. B. Renó, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00066-5 308, 249 (2003).
64. J. M. C. Malbouisson and B. Baseia, Phys. Scr. PHSTBO 0031-8949 10.1238/Physica.Regular.067a00093 67, 93 (2003).
65. A. Kenfack and K. Życzkowski, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/6/10/003 6, 396 (2004).
66. J. K. Asbóth, J. Calsamiglia, and H. Ritsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.173602 94, 173602 (2005).
67. M. Boca, I. Ghiu, P. Marian, and T. A. Marian, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.014302 79, 014302 (2009).
68. E. Shchukin and W. Vogel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.230502 95, 230502 (2005).
69. A. Miranowicz and M. Piani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.058901 97, 058901 (2006).
70. A. Miranowicz, M. Piani, P. Horodecki, and R. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.052303 80, 052303 (2009).
71. J. Rigas, O. Gühne, and N. Lütkenhaus, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012341 73, 012341 (2006).
72. J. K. Korbicz and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022318 74, 022318 (2006).
73. T. Moroder, M. Keyl, and N. Lütkenhaus, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/41/27/275302 41, 275302 (2008).
74. H. Häseler, T. Moroder, and N. Lütkenhaus, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.032303 77, 032303 (2008).
75. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2722 84, 2722 (2000).
76. M. Hillery and M. S. Zubairy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.050503 96, 050503 (2006).
77. R. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2726 84, 2726 (2000).
78. S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.120401 88, 120401 (2002).
79. U. M. Titulaer and R. J. Glauber, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.140.B676 140, B676 (1965).
80. A. Wünsche, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/6/2/006 6, 159 (2004).
81. T. Kiesel, W. Vogel, V. Parigi, A. Zavatta, and M. Bellini, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.021804 78, 021804 (R) (2008).
82. J. K. Korbicz, J. I. Cirac, J. Wehr, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.153601 94, 153601 (2005).
83. J. Sperling (private communication).
84. G. Strang, Linear Algebra and Its Applications (Academic Press, New York, 1980).
85. E. Shchukin and W. Vogel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.030302 74, 030302 (R) (2006).
86. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.865 81, 865 (2009).
87. M. G. Raymer, A. C. Funk, B. C. Sanders, and H. de Guise, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052104 67, 052104 (2003).
88. G. S. Agarwal and A. Biswas, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/7/11/006 7, 350 (2005).
89. L. Song, X. Wang, D. Yan, and Z. S. Pu, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/41/1/015505 41, 015505 (2008).
90. E. Schrödinger, Sitz. Ber. Preuss. Akad. Wiss. (Phys.-Math. Kl.) 19, 296 (1930);
91. H. R. Robertson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.46.794 46, 794 (1934).
92. R. F. Muirhead, Proc. Edinburgh Math. Soc. PEMSA3 0013-0915 10.1017/S001309150003460X 21, 144 (1903).
93. M. A. Berger, An Introduction to Probability and Stochastic Processes (Springer, New York, 1993).