Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics |
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Authors: | Fan Hong-yi Hu Li-yun Wang Ji-suo |
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Affiliation: | Department of Physics, Shangai Jiao Tong University, Shangai, China. |
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Abstract: | We employ the recently established basis (the two-variable Hermite-Gaussian function) of the generalized Bargmann space (BGBS) [Phys. Lett. A303, 311 (2002)] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT. |
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