Authors
Abstract
In this paper, we construct the Gazeau-Klauder coherent states of a two- dimensional harmonic oscillator on a sphere based on two equivalent approaches. First, we consider the oscillator on the sphere as a deformed (non-degenerate) one-dimensional oscillator. Second, the oscillator on the sphere is considered as the usual (degenerate) two--dimensional oscillator. Then, by investigating the quantum optical properties of the constructed coherent states, we study the effect of the space curvature on the properties of the constructed sphere Gazeau-Klauder coherent states, according to these two approaches.
Keywords
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4. P Deuar and P D Drummond, Phys. Rev. A 66 (2002) 033812.
5. C C Chong, D I Tsomokos, and A Vourdas, Phys. Rev. A 66 (2002) 033813.
6. R Roknizadeh and M K Tavassoly, J. Phys. A 37 (2004) 5649.
7. J-P Gazeau and J R Klauder, J. Phys. A 32 (1999) 123.
8. J-P Gazeau and P Monceau, “Generalized Coherent States for Arbitrary Quantum Systems”, Klauer Academic Publishers, Printed in the Netherlands (2000)..
9. R Roknizadeh and M K Tavassoly, J. Phys. A 37, (2004) 8111.
10. D Popov, Phys. Lett. A 316 (2003) 369.
11. J-P Antoine, J-P Gazeau, J R Klauder, P Monceau, and K A Penson, J. Math. Phys. 42 (2001) 2349.
12. A H El Kinani and M Daoud, J. Math. Phys. 35 (2001) 2279, J. Phys. A 34 (2001) 5373.
13. A H El Kinani and M Daoud, Int. J. Mod. Phys. B 16 (2002) 3915.
14. A H El Kinani and M Daoud, Int. J. Mod. Phys. B 15 (2003) 2465.
15. P W Higgs, J. Phys. A: Math. Gen. 12 (1979) 309.
16. A Mahdifar, R Roknizadeh and M H Naderi, J. Phys. A: Math. Gen. 39 (2006) 7003.
17. J P Gazeau and R Klauder, J. Phys. A: Math. Gen. 32 (1999).
18. R Roknizadeh, M K Tavassoly, J. Math. Phys. 46 (2005) 042110.
19. I S Gradshteyn, I M Ryzhik, Table of Integrals and Series, Academic Press (1980).
20. L Mandel and E Wolf, “Optical Coherence and Quantum Optics”, Cambridge University Press, Cambridge (1995).
21. M O Scully and M S Zubairy, “Quantum optics”, Cambridge University Press, Cambridge (1997).
22. G S Agarwal and K Tara, Phys. Rev. A 43 (1991) 429.
23. L Dello Sbarba and V Hussin, J. Math. Phys. 48 (2007) 012110.
24. G R Honarasa, M K Tavassoly, M Hatami and R Roknizadeh, Physica A 390 (2011) 1381.
25. L Mandel, Opt. Lett. 4 (1979) 205.
26. D T Pegg and S M Barnett, Phys. Rev. A 39 (1989) 1665.
27. G.R. Honarasa, M.K. Tavassoly, M. Hatami, Optics Communications 282 (2009) 2192
3. S Twareqe Ali, J-P Antoine, and J-P Gazeau, “Coherent States, Wavelets and Their Generalizations”, Springer-Verlag, New York, (2000).
4. P Deuar and P D Drummond, Phys. Rev. A 66 (2002) 033812.
5. C C Chong, D I Tsomokos, and A Vourdas, Phys. Rev. A 66 (2002) 033813.
6. R Roknizadeh and M K Tavassoly, J. Phys. A 37 (2004) 5649.
7. J-P Gazeau and J R Klauder, J. Phys. A 32 (1999) 123.
8. J-P Gazeau and P Monceau, “Generalized Coherent States for Arbitrary Quantum Systems”, Klauer Academic Publishers, Printed in the Netherlands (2000)..
9. R Roknizadeh and M K Tavassoly, J. Phys. A 37, (2004) 8111.
10. D Popov, Phys. Lett. A 316 (2003) 369.
11. J-P Antoine, J-P Gazeau, J R Klauder, P Monceau, and K A Penson, J. Math. Phys. 42 (2001) 2349.
12. A H El Kinani and M Daoud, J. Math. Phys. 35 (2001) 2279, J. Phys. A 34 (2001) 5373.
13. A H El Kinani and M Daoud, Int. J. Mod. Phys. B 16 (2002) 3915.
14. A H El Kinani and M Daoud, Int. J. Mod. Phys. B 15 (2003) 2465.
15. P W Higgs, J. Phys. A: Math. Gen. 12 (1979) 309.
16. A Mahdifar, R Roknizadeh and M H Naderi, J. Phys. A: Math. Gen. 39 (2006) 7003.
17. J P Gazeau and R Klauder, J. Phys. A: Math. Gen. 32 (1999).
18. R Roknizadeh, M K Tavassoly, J. Math. Phys. 46 (2005) 042110.
19. I S Gradshteyn, I M Ryzhik, Table of Integrals and Series, Academic Press (1980).
20. L Mandel and E Wolf, “Optical Coherence and Quantum Optics”, Cambridge University Press, Cambridge (1995).
21. M O Scully and M S Zubairy, “Quantum optics”, Cambridge University Press, Cambridge (1997).
22. G S Agarwal and K Tara, Phys. Rev. A 43 (1991) 429.
23. L Dello Sbarba and V Hussin, J. Math. Phys. 48 (2007) 012110.
24. G R Honarasa, M K Tavassoly, M Hatami and R Roknizadeh, Physica A 390 (2011) 1381.
25. L Mandel, Opt. Lett. 4 (1979) 205.
26. D T Pegg and S M Barnett, Phys. Rev. A 39 (1989) 1665.
27. G.R. Honarasa, M.K. Tavassoly, M. Hatami, Optics Communications 282 (2009) 2192
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