Abstract
This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions. These states satisfy all required mathematical and physical properties. The associated Stieltjes power-moment problem is explicitly solved by using Meijer’s G-function and the Mellin inversion theorem. Relevant quantum optical and thermal characteristics are investigated. The formalism is applied to particular cases of the associated Hermite, Laguerre, Jacobi polynomials and hypergeometric functions. Their corresponding states exhibit sub-Poissonian photon number statistics.
Graphical abstract
Similar content being viewed by others
References
E. Schrödinger, Naturwissenschaften 14, 664 (1926)
R.J. Glauber, Phys. Rev. 130, 2529 (1963)
R.J. Glauber, Phys. Rev. 131, 2766 (1963)
J.R. Klauder, J. Math. Phys. 4, 1055 (1963)
J.R. Klauder, J. Math. Phys. 4, 1058 (1963)
E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)
A.O. Barut, L. Girardello, Commun. Math. Phys. 21, 41 (1971)
A.M. Perelomov,Generalized coherent states and their applications (Springer, Berlin, 1986)
S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations 2nd edition, Theoretical and Mathematical Physics (Springer, New York, 2014)
S.T. Ali, J.-P. Antoine, J.-P. Gazeau, U. A. Mueller, Rev. Math. Phys. 7, 1013 (1995)
J.R. Klauder, B.S. Skagerstam,Coherent states: applications in physics and mathematical physics (World Sientific, Singapore, 1985)
J.-P. Gazeau,Coherent states in quantum physics (Wiley-, Weinheim, 2009)
F.A. Berezin,The method of Second Quantization (Nauka, Moscow, 1986)
I. Aremua, J-P. Gazeau, M.N. Hounkonnou, J. Phys. A: Math. Gen. 45, 335302 (2012)
I. Aremua, M. N. Hounkonnou, E. Baloïtcha, Rep. Math. Phys. 45, 247 (2015)
N. Cotfas, J. Phys. A: Math. Gen. 35, 9355 (2002)
A.N.F. Aleixo, A.B. Balantekin, J. Phys. A: Math. Gen. 37, 8513 (2004)
M.N. Hounkonnou, K. Sodoga, J. Phys. A: Math. Gen 38, 7851 (2005)
G.S. Agarwal, K. Tara, Phys. Rev A. 43, 492 (1991)
G.S. Agarwal, K. Tara, Phys. Rev A. 46, 485 (1992)
V.V. Dodonov, Ya A. Korennoy, V. I. Man’ko, Y. A. Moukhin, Quantum Semiclass. Opt. 8, 413 (1996)
V.V. Dodonov, J. Opt. B: Quantum Semiclass. 4, R1 (2002)
V.V. Dodonov, V.I. Man’ko,Theory of Nonclassical States of Light (Taylor and Francis, London, 2003)
J.M. Sixdeniers, K.A. Penson, J. Phys. A. Math. Gen. 34, 2859 (2001)
J.R. Klauder, K.A. Penson, J.M. Sixdeniers, Phys. Rev. A 64, 013817 (2001)
D. Popov, J. Phys. A: Math. Gen. 35, 7205 (2002)
D. Popov, I. Zaharie, S.H. Dong, Czech. J. Phys. 56, 157 (2006)
D. Popov, Electron. J. Theor. Phys. (EJTP) 3, 123 (2006)
M.N. Hounkonnou, E.B. Ngompe Nkouankam, J. Phys A: Math. Theor. 42, 025206 (2009)
T. Appl, D.H. Schiller, J. Phys. A: Math. and Gen. 37, 2731 (2004)
B. Mojaveri, A. Dehghani, S. Mahmoodi, Phys. Scr. 89, 085202 (2014)
S. Dey, V. Hussin, Phys. Rev. A. 93, 053824 (2016)
V.I. Man’ko, G. Marmo, E.C.G. Sudarshan, F. Zaccaria, Phys. Scr. 55, 528 (1997)
V.I. Man’ko, G. Marmo, S. Solimeno, F. Zaccaria, Int. J. Mod. Phys. A 8, 3577 (1993)
V.I. Man’ko, G. Marmo, S. Solimeno, F. Zaccaria, Phys. Lett. A 176, 173 (1993)
K. Sodoga, M.N. Hounkonnou, I. Aremua, Eur. Phys. J. D 72, 105 (2018)
A.F. Nikiforov, S.K. Suslov, V.B. Uvarov,Classical Orthogonal Polynomials of a Discrete Variable (Berlin, Springer, 1991)
M. Daoud, Phys. Lett. A. 305, 135 (2002)
K. Berrada, J. Math. Phys 56, 072104 (2015)
O.I. Marichev, Handbook of integral transforms of higher transcendental functions: theory and algorithmic tables (Ellis Harwood, Chichester, UK, 1983)
A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev,Integrals and series (Gordon and Breach, New York, 1998)
L. Mandel, E. Wolf,Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995)
K.A. Penson, A.I. Solomon, J. Math. Phys. 40, 2354 (1999)
A.M. Mathai, R.K. Saxena, Generalized hypergeometric functions with applications in statistics and physical sciences, Lecture Notes in Mathematics (Springer, Berlin, 1973), vol 348
Y.L. Luke,The special functions and their approximations, (Academic Press, California, 1969), vol 1
S-H. Dong,Factorization Method in Quantum Mechanics, (Springer, Dordrecht, 2007),
C.M. Joshi, J.B. McDonald, J. Math. Anal. Appl. 40, 278 (1972)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sodoga, K., Aremua, I. & Hounkonnou, M.N. Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties. Eur. Phys. J. D 72, 172 (2018). https://doi.org/10.1140/epjd/e2018-90230-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2018-90230-8