Special Issue: Advances in Foundations of Quantum Mechanics and Quantum Information with atoms and photons, QUANTUM 2014No Access

Emerging quantum mechanics: Coefficient of second-order coherence from classical random fields interacting with threshold type detectors

Andrei Khrennikov

Andrei Khrennikov

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, S-35195, Växjö-Kalmar, Sweden

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https://doi.org/10.1142/S0219749915600072Cited by:0 (Source: Crossref)

Abstract

This paper is a contribution to the project "emergent quantum mechanics" unifying a variety of attempts to treat quantum mechanics (QMs) as emergent from other theories pretending on finer descriptions of quantum phenomena. More concretely it is about an attempt to model detection probabilities predicted by QM for single photon states by using classical random fields interacting with detectors of the threshold type. Continuous field model, prequantum classical statistical field theory (PCSFT), was developed in recent years and its predictions about probabilities and correlations match well with QM. The main problem is to develop the corresponding measurement theory which would describe the transition from continuous fields to discrete events, "clicks of detectors". Some success was achieved and the click-probabilities for quantum observables can be derived from PCSFT by modeling interaction of fields with the threshold type detectors. However, already for the coefficient of second-order coherence g²(0) calculations are too complicated and only an estimation of g²(0) was obtained. In this paper, we present results of numerical simulation based on PCSFT and modeling of interaction with threshold type detectors. The "prequantum random field" interacting with a detector is modeled as the Brownian motion in the space of classical fields (Wiener process in complex Hilbert space). Simulation for g²(0) shows that this coefficient approaches zero with increase of the number of detections.

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References

G. Grössing, H.-T. Elze, J. M. Pascasio and J. Walleczek (eds.), J. Phys.: Conf. Ser. 504 (2014) 011001 . Google Scholar
A. Khrennikov , Beyond Quantum ( Pan Stanford Publ. , Singapore , 2014 ) . Crossref, Google Scholar
G. Jaeger et al. (eds.) , Advances in Quantum Theory, AIP Conf. Proc. 1327 ( Melville , NY , 2011 ) . Google Scholar
A. Khrennikov (ed.) , Quantum Theory: Reconsideration of Foundations-5, AIP Conf. Proc. 1232 ( Melville , NY , 2010 ) . Google Scholar
(eds.) , Foundations of Probability and Physics-5, AIP Conf. Proc. 1101 ( Melville , NY , 2009 ) . Google Scholar
(eds.) , Quantum Theory: Reconsideration of Foundations-4, AIP Conf. Proc. 962 ( Melville , NY , 2008 ) . Google Scholar
G. Adenier , C. Fuchs and A. Khrennikov (eds.) , Foundations of Probability and Physics-4, AIP Conf. Proc. 889 ( Melville , NY , 2007 ) . Google Scholar
G. Brida et al. , J. Phys. B: At. Mol. Opt. Phys. 35 , 4751 ( 2002 ) . Crossref, Web of Science, Google Scholar
G. Brida et al. , J. Phys. B: At. Mol. Opt. Phys. 37 , 3781 ( 2004 ) . Crossref, Web of Science, Google Scholar
Brida et al. , Int. J. Quantum Inform. 5 , 265 ( 2007 ) . Link, Web of Science, Google Scholar
G. Brida et al. , Opt. Exp. 16 , 11750 ( 2008 ) . Crossref, Web of Science, Google Scholar
M. Genovese et al. , J. Phys.: Conf. Ser. 67 , 01204 ( 2007 ) . Crossref, Google Scholar
U. Sinhaet al., Testing Born's rule in quantum mechanics with a triple slit experiment, Foundations of Probability and Physics-5, AIP Conf. Proc.1101, eds. L. Accardiet al. (Melville, NY, 2009) pp. 200–207. Google Scholar
Reconstruction of mode structure of faint light sources and its applications, S. Polyakov, E. Goldschmidt, A. Migdall, S. Kueck, F. Piacentini, G. Brida, I. Degiovanni, I. Berchera and M. Genovese, Phys. Scripta (2014), to be published . Google Scholar
K. Michielsen and H. De Raedt, Quantum Theory: Reconsiderations of Foundations-5 1232, ed. A. Khrennikov (American Institute of Physics, Melville, NY, 2010) p. 27. Google Scholar
K. Michielsen et al. , Physica Scripta T 151 , 014005 ( 2012 ) . Crossref, Web of Science, Google Scholar
G. M. D'Ariano, Operational axioms for QM, Foundations of Probability and Physics-4, AIP Conf. Proc.889, eds. G. Adenier, C. Fuchs and A. Khrennikov (Melville, NY, 2007) pp. 79–105. Google Scholar
A. Khrennikov , J. Phys. A: Math. Gen. 38 , 9051 ( 2005 ) . Crossref, Google Scholar
A. Khrennikov , Found. Phys. Lett. 18 , 637 ( 2006 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , Phys. Lett. A 357 , 171 ( 2006 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , Found. Phys. Lett. 19 , 299 ( 2006 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , Nuovo Cimento B 121 , 505 ( 2006 ) . Google Scholar
A. Khrennikov , EPL 88 , 40005.1 ( 2009 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , EPL 90 , 40004 ( 2010 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov, J. Russ. Laser Res. 31(2), 191 (2010). Crossref, Web of Science, Google Scholar
A. Khrennikov , M. Ohya and N. Watanabe , Int. J. Quantum Inform. 9 , 281 ( 2011 ) . Link, Web of Science, Google Scholar
A. Khrennikov , M. Ohya and N. Watanabe , J. Russ. Laser Res. 31 , 462 ( 2010 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , J. Modern Optics 59 , 667 ( 2012 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , B. Nilsson and S. Nordebo , Int. J. Quantum Inform. 10 , 1241014 ( 2012 ) . Link, Web of Science, Google Scholar
A. Khrennikov , Annals of Physics 327 , 1786 ( 2012 ) . Crossref, Web of Science, Google Scholar
A. Khrennikov , B. Nilsson and S. Nordebo , J. Phys.: Conf. Ser. 361 , 012030 ( 2012 ) . Crossref, Google Scholar
L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge Univ. Press , Cambridge , 1995 ) . Crossref, Google Scholar
P. Grangier , Etude expérimentale de propriétés non-classiques de la lumière: interférence à un seul photon ( Université de Paris-Sud , Centre D'Orsay , 1986 ) . Google Scholar
P. Grangier , G. Roger and A. Aspect , EPL 1 , 173 ( 1986 ) . Crossref, Web of Science, Google Scholar
M. Beck , J. Opt. Soc. Am. B 24 , 2972 ( 2007 ) . Crossref, Web of Science, Google Scholar
A. Ling et al. , Opt. Exp. 17 , 21302 ( 2009 ) . Crossref, Web of Science, Google Scholar
S. V. Polyakov, A. Migdall and Sae Woo Nam, Advances in Quantum Theory, AIP Conf. Proc.1327 (Melville, NY, 2010) pp. 505–519. Google Scholar
M. D. Eisaman et al. , Rev. Sci. Instrum. 82 , 071101 ( 2011 ) . Crossref, Web of Science, Google Scholar
N. Bohr , The philosophical writings of Niels Bohr 3 ( Ox Bow Press , Woodbridge, Conn. , 1987 ) . Google Scholar
A. Khrennikov , Nuovo Cimento B 121 , 505 ( 2006 ) . Google Scholar