×

Negative values of quasidistributions and quantum wave and number statistics. (English) Zbl 1390.81773

Summary: We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

MSC:

81V80 Quantum optics
81P40 Quantum coherence, entanglement, quantum correlations
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Glauber, R. J., Phys. Rev., 130, 2529, (1963) · doi:10.1103/PhysRev.130.2529
[2] Glauber, R. J., Phys. Rev., 131, 2766, (1963) · Zbl 1371.81166 · doi:10.1103/PhysRev.131.2766
[3] Cahill, K. E.; Glauber, R. J., Phys. Rev., 177, 1857, (1969) · doi:10.1103/PhysRev.177.1857
[4] Cahill, K. E.; Glauber, R. J., Phys. Rev., 177, 1882, (1969) · doi:10.1103/PhysRev.177.1882
[5] Agarwal, G. S.; Wolf, E., Phys. Rev. D, 2, 2161, (1970) · doi:10.1103/PhysRevA.2.2161
[6] Agarwal, G. S.; Wolf, E., Phys. Rev. D, 2, 2187, (1970) · Zbl 1227.81197 · doi:10.1103/physrevd.2.2187
[7] Agarwal, G. S.; Wolf, E., Phys. Rev. D, 2, 2206, (1970) · Zbl 1227.81198 · doi:10.1103/physrevd.2.2206
[8] Shchukin, E. V.; Vogel, W., Phys. Rev. A, 72, (2005) · doi:10.1103/PhysRevA.72.043808
[9] Miranowicz, A.; Bartkowiak, M.; Wang, X.; Yu-xi, Liu; Nori, F., Phys. Rev. A, 82, (2010) · doi:10.1103/PhysRevA.82.013824
[10] Peřina, J.; Křepelka, J., J. Optics B, 7, 246, (2005) · doi:10.1088/1464-4266/7/9/003
[11] Peřina, J.; Křepelka, J., J. Found. Phys. Chem., 1, 158, (2011)
[12] Peřina, J.; Křepelka, J., Int. J. Theor. Math. Phys., 4, 88, (2014) · doi:10.5923/j.ijtmp.20140403.03
[13] Peřina, J.; Křepelka, J., Opt. Commun., 326, 10, (2014) · doi:10.1016/j.optcom.2014.04.009
[14] Arkhipov, I. I.; Peřina, J. Jr; Peřina, J.; Miranowicz, A., Phys. Rev. A, 91, (2015) · doi:10.1103/PhysRevA.91.033837
[15] Haderka, O.; Peřina, J. Jr; Hamar, M.; Peřina, J., Phys. Rev. A, 71, (2005) · doi:10.1103/PhysRevA.71.033815
[16] Peřina, J.; Křepelka, J.; Peřina, J. Jr; Bondani, M.; Allevi, A.; Andreoni, A., Phys. Rev. A, 76, (2007) · doi:10.1103/PhysRevA.76.043806
[17] Peřina, J.; Křepelka, J.; Peřina, J. Jr; Bondani, M.; Allevi, A.; Andreoni, A., Eur. Phys. J. D, 53, 373, (2009) · doi:10.1140/epjd/e2009-00136-3
[18] Peřina, J. Jr; Hamar, M.; Michálek, V.; Haderka, O., Phys. Rev. A, 85, (2012) · doi:10.1103/PhysRevA.85.023816
[19] Peřina, J. Jr; Haderka, O.; Michálek, V.; Hamar, M., Phys. Rev. A, 87, (2013) · doi:10.1103/PhysRevA.87.022108
[20] Allevi, A.; Lamperti, M.; Bondani, M.; Peřina, J. Jr; Michálek, V.; Haderka, O.; Machulka, R., Phys. Rev. A, 88, (2013) · doi:10.1103/PhysRevA.88.063807
[21] Peřina, J.; Křepelka, J., Phys. Lett. A, 380, 1932, (2016) · doi:10.1016/j.physleta.2016.04.007
[22] Peřina, J., Quantum Statistics of Linear and Nonlinear Optical Phenomena, (1991), Dordrecht: Kluwer, Dordrecht
[23] Agudelo, E.; Sperling, J.; Vogel, W.; Köhnke, S.; Mraz, M.; Hage, B., Phys. Rev. A, 92, (2015) · doi:10.1103/PhysRevA.92.033837
[24] Morse, P. M.; Feshbach, H., Methods of Theoretical Physics, vol I, (1953), Amsterdam: McGraw-Hill, Amsterdam · Zbl 0051.40603
[25] Peřina, J.; Křepelka, J., Opt. Commun., 281, 4705, (2008) · doi:10.1016/j.optcom.2008.06.007
[26] Gamo, H.; Wolf, E., Progress in Optics, vol 3, p 187, (1964), Amsterdam: North-Holland, Amsterdam
[27] Leonhardt, U., Measuring the Quantum State of Light, (1997), Cambridge: Cambridge University Press, Cambridge
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.