Abstract
We develop a general approach to building photon-added generalized Peremolov coherent states (PAGPCSs) and photon-added generalized Barut–Girardello coherent states (PA-GBGCSs) associated to generalized su(1, 1) algebra. We study the problem of completeness of these coherent states for some particular cases and investigate the physical properties of these states through the evaluation of the Mandel parameter using an alteration of the Holstein–Primakoff realization of the su(1, 1) algebra. We show that these states exhibit sub-Poissonian, Poissonian, or super-Poissonian statistics. These features make the photon-added approach a good candidate for implementation of quantum optics schemes and coherent information processing.
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References
E. Schrödinger, Naturwissenschaften, 14, 664 (1926).
R. Glauber, Phys. Rev., 130, 2529 (1963).
R. Glauber, Phys. Rev., 131, 2766 (1963).
J. R. Klauder, J. Math. Phys., 4, 1055 (1963).
J. R. Klauder, J. Math. Phys., 4, 1058 (1963).
J. R. Klauder and B.-S. Skagertan, Coherent States, World Scientific, Singapore (1985).
A. M. Perelomov, Generalized Coherent States and Their Applications, Springer, Berlin (1986).
S. T. Ali, J.-P. Antoine, and J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations, Springer, New York (2000).
A. M. Perelomov, Commun. Math. Phys., 26, 222 (1972).
R. Gilmore, Ann. Phys. (NY), 74, 391 (1972).
K. Berrada, Phys. Rev. A, 88, 013817 (2013).
K. Berrada, Chin. Phys. B, 23, 024208 (2014).
K. Berrada, Phys. Rev. A, 88, 035806 (2013).
V. G. Drinfeld, ”Quantum groups,” in: Proceedings of the International Congress of Mathematics, Berkeley, 1986, American Mathematical Society (1987), p. 798.
M. Jimbo, Lett. Math. Phys., 10, 63 (1985).
M. El Baz, Y. Hassouni and F. Madouri, Rep. Math. Phys., 50, 263 (2002).
V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, Phys. Scr., 55, 528 (1997).
B. Jurčo, Lett. Math. Phys., 21, 51 (1991).
D. Ellinas, J. Phys. A: Math. Gen., 26, L543 (1993).
L. C. Biedenharn, J. Phys. A: Math. Gen., 22, L873 (1989).
A. J. Macfarlane, J. Phys. A: Math. Gen., 22, 4581 (1989).
M. Arik and D. D. Coon, J. Math. Phys., 17, 4581 (1976).
A. M. Perelomov, Helv. Phys. Acta, 68, 554 (1996).
R. Chakrabarti and R. Jagannathan, J. Phys. A: Math. Gen., 24, 554 (1991).
R. Chakrabarti and S. Vasan, J. Phys. A: Math. Gen., 37, 10561 (2004).
M. El Baz et Y. Hassouni, Phys. Lett. A, 300, 361 (2002).
G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge University Press (1990), p. 35.
J. P. Gazeau and B. Champagne, “The Fibonacci-deformed harmonic oscillator in algebraic methods in physics,” in: Y. Saint-Aubin and L. Vinet (Eds.), Algebraic Methods in Physics, CRM Series in Theoretical and Mathematical Physics, Springer, Berlin (2000), Vol. 3.
G. S. Agarwal and K. Tara, Phys. Rev. A., 43, 492 (1991).
V. V. Dodonov, M. A. Marchiolli, Ya. A. Korennoy, et al., Phys. Rev. A, 58, 4087 (1998).
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press (1995).
J. Katriel and A. I. Solomon, Phys. Rev. A, 49, 5149 (1994).
K. Berrada, M. El Baz, F. Saif, et al., J. Phys. A: Math. Gen., 42, 285306 (2009).
M. Bellini, A. S. Coelho, S. N. Filippov, et al., Phys. Rev. A, 85, 052129 (2012).
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Alrajhi, M.A. General Approach to the Construction of Photon-Added SU(1,1) Coherent States. J Russ Laser Res 35, 570–581 (2014). https://doi.org/10.1007/s10946-014-9464-x
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DOI: https://doi.org/10.1007/s10946-014-9464-x