论文部分内容阅读
By converting the triangular functions in the integration keel of the fractional Fourier transformation to the hy-perbolic function, i.e., tanα→tanhα, sinα→sinhα, we find quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within ordered product of operators (IWOP) wederive the unitary operator responsible for the FrST, which is composite and is made of eiπa?a/2 and exp[ iα2 (a2+a?2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.