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Inspired by the wavelet transform in quantum mechanics, we define the new Ridgelet transform for quantum optics by rewriting the classic Ridgelet transform via the two-mode coordinate representation in Fock space. Furthermore, we give the explicit form of the asymmetric operator's integral and derive two useful formulas for the normal ordering of the two-mode operator with the help of the technique of integration within an ordered product (IWOP) of operators. By choosing the two-variable Mexican hat's mother wavelet function, we analyse the Ridgelet transforms of the coherent state, special squeezed coherent state, intermediary entangled state on the basis of the theories we have mentioned.
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Keywords:
- the IWOP technique /
- Ridgelet transform /
- coherent state
[1] Candes E J 1999 Ridgelets and Their Derivatives Representation of Images with Edges Department of Statistics, Stanford University, Saint-Malo Proceedings and Larry L. Schumaker(eds), p1-10.
[2] Starck J L, Candés E J, Donoho D L 2002 Trans. Image Processin 11 670
[3] Starck J L, Donoho D L, Candes E J 2003 Astronomy & Astrophysics 398 785
[4] Chuang I L, Nielsen M A 2000 Quantum computation and quantum information (Cambridge University Press, Cambridge)
[5] Fan H Y, Lu H L 2006 Optics Commun 258 51
[6] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[7] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[8] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[9] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[10] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 147
[11] Song J, Xu Y J, Fan H Y 2011 Acta Phys. Sin. 60 084208 (in Chinese) [宋军, 许业军, 范洪义 2011 60 084208]
[12] Yu H J, Du J M, Zhang X L 2012 Acta Phys. Sin. 61 164205 (in Chinese) [余海军, 杜建明, 张秀兰 2012 61 164205]
[13] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[14] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[15] Fan H Y 2003 Journal of Optics B: Quant. & Semi. Opt. 5 147-R163
[16] Fan H Y 1990 Phys. Rev. A 41 1526
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[1] Candes E J 1999 Ridgelets and Their Derivatives Representation of Images with Edges Department of Statistics, Stanford University, Saint-Malo Proceedings and Larry L. Schumaker(eds), p1-10.
[2] Starck J L, Candés E J, Donoho D L 2002 Trans. Image Processin 11 670
[3] Starck J L, Donoho D L, Candes E J 2003 Astronomy & Astrophysics 398 785
[4] Chuang I L, Nielsen M A 2000 Quantum computation and quantum information (Cambridge University Press, Cambridge)
[5] Fan H Y, Lu H L 2006 Optics Commun 258 51
[6] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[7] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[8] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[9] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[10] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 147
[11] Song J, Xu Y J, Fan H Y 2011 Acta Phys. Sin. 60 084208 (in Chinese) [宋军, 许业军, 范洪义 2011 60 084208]
[12] Yu H J, Du J M, Zhang X L 2012 Acta Phys. Sin. 61 164205 (in Chinese) [余海军, 杜建明, 张秀兰 2012 61 164205]
[13] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[14] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[15] Fan H Y 2003 Journal of Optics B: Quant. & Semi. Opt. 5 147-R163
[16] Fan H Y 1990 Phys. Rev. A 41 1526
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