On the entangled fractional squeezing transformation

摘要

We propose an entangled fractional squeezing transformation (EPrST) generated by using two mutually conjugate entangled state representations with the following operator: e~(-iα(a_1~+a_2~+ + a_1a_2))e~(iπa_2~+a_2); this transformation sharply contrasts the complex fractional Fourier transformation produced by using e~(-iα(a_1~+a_1 + a_2~+a_2))e~(iπa_2~+a_2) (see Front. Phys. DOI 10.1007/s11467-014-0445-x). The EFrST is obtained by converting the triangular functions in the integration kernel of the usual fractional Fourier transformation into hyperbolic functions, i.e., tan α → tanh α and sin α → sinh α. The fractional property of the EFrST can be well described by virtue of the properties of the entangled state representations.