STARKOV V.N., SEMENOV A.A., GOMONAY E.V.
ABSTRACT
Using methods of computational physics the algorithm is implemented that allows investigating the ill-posed problem of noise reduction, connected with losses, dark counts and background radiation in photocounting statistics of quantum light. The regularizing operator in operator equation of the first kind allows direct restoration of photon distribution function from photon-number statistics with known noise parameters. This is confirmed by computational experiments.
KEYWORDS
quantum optics, photon probability, ill-posed problem, the operator.
REFERENCES
1. Waks, E., Diamanti, E., Sanders, B.C. and et al. (2004), “Direct Observation of Non-classical Photon Statistics in Parametric Downconversion”, Phys. Rev. Lett., no. 92, 113602.
2. Achilles, D., Silberhoen, C., Sliwa, C. and et al. (2003), “Fiber-assisted Detection with Photon Number Resolution”, Opt. Lett., no. 28 (23):2387-9.
3. Sperling, J., Vogel, W. and Agarwal, G.S. (2013), “Correlation Measurements with on-off Detectors”, Phys. Rev., A 88, 043821.
4. Sperling, J., Vogel, W. and Agarwal, G.S. (2012), “Sub-Binomial Light”, Phys. Rev. Lett., 109, 093601.
5. Mandel, L. and Wolf, E. (1995), Optical Coherence and Quantum Optics, Cambridge University Press.
6. Starkov, V.N., Semenov, A.A. and Gomonay, H.V. (2009), “Numerical Reconstruction of Photon-number Statistics from Photo counting Statistics: Regularization of an Ill-posed Problem”, Phys. Rev., A 80, 013813.
7. Semenov, A.A., Turchin, A.V., Gomonay, H.V. (2008), “Detection of Quantum Light in the Presence of Noise”, Phys. Rev., A 78, 055803.
8. Welsch, D.-G., Vogel, W. and Opartny, T. (1999), “Homodyne Detection and Quantum State Reconstruction”, Progress in Optics, no. 39, pp. 63. 2. ... A 261, 20.
9. Mandel, L. (1982), “Squeezed States and Sub-Poissonian Photon Statistics”, Phys. Rev. Lett., no. 49, p. 136.
10. Akhiezer, N.I. and Glazman, I.M. (1966), Teoriya lineynykh operatorov v gilbertovom prostranstve [The theory of linear operators in Hilbert space], Nauka, Moscow, Russia.
11. Kolmogorov, A.N. and Fomin, S.V. (1972), Elementy teorii funktsiy i funktsionalnogo analiza [Elements of the theory of functions and functional analysis], Nauka, Moscow, Russia.
12. Tikhonov, A.N. and Arsenin, V.Ya. (1966), Metody resheniya nekorrektnykh zadach [Methods of solving ill-posed problems], Nauka, Moscow, Russia.
13. Verlan, A.F. and Sizikov, V.S. (1986), Integralnye uravneniya: metody, algoritmy, programmy. Spravochnoe posobie [Integral equation methods, algorithms, programs. Reference manual], Naukova dumka, Kiev, Ukraine.
14. Vasin, V.V. and Ageev, A.L. (1993), Nekorrektnye zadachi s apriornoy informatsiey [Ill-posed problems with a priori information], Uralskaya izdatelskaya firma «Nauka», Ekaterinburg, Russia.
15. Sizikov, V.S. (2011), Obratnye prikladnye zadachi i MatLab: Uchebnoe posobie [Inverse application problems and MatLab: Textbook], Lan, St. Petersburg, Russia.
16. Lowes, A.K. (1989), Inverse und schlecht gestellte probleme, Teubner, Stuttgart, Germany.
17. Bakushinskiy, A.B. and Goncharskiy, A.V. (1989), Nekorrektnye zadachi. Chislennye metody i prilozheniya [Ill-posed problems. Numerical methods and applications], Izd-vo Mosk. un-ta, Moscow, Russia.
18. Vaynikko, G.M. and Veretennikov, A.Yu. (1986), Iteratsionnye protsedury v nekorrektnykh zadachakh [Iterative procedures for ill-posed problems], Nauka, Moscow, Russia.
19. Morozov, V.A. (1974), Regulyarnye metody resheniya nekorrektno postavlennykh zadach [Regular methods for solving ill-posed problems], Izd-vo Mosk. un-ta, Moscow, Russia.
20. Goncharskiy, A.V., Leonov, A.S. and Yagola, A.G. (1973), “Generalized discrepancy principle”, Zhurn. vychisl. matematiki i mat. fiziki, Vol. 13, no. 2, pp. 294-302.
21. Defrise, M. and De Mol, C. (1987), “A Note on Stopping Rules for Iterative Methods and Filtered svd”, Inverse Problems: An Interdisciplinary Study, pp. 261-268.