title: Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics.
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.
authors.affiliation: Department of Physics, Shangai Jiao Tong University, Shangai, China.
authors.forename: Hong-yi
authors.initials: HY
authors.lastname: Fan
authors.forename: Li-yun
authors.initials: LY
authors.lastname: Hu
authors.forename: Ji-suo
authors.initials: JS
authors.lastname: Wang