From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

Hu, Liyun Liyun, Fan Fan +1 more

Ke Zhang, Chengyu Fan, Hong-Yi Fan

Cui-hong Lv, Hong-Yi Fan, Dongwei Li

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tan α → tanh α , sin α → sinh α , we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of e i πa † a /2 and exp . The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

Hong-Yi, Fan Fan, Junhua +3 more

Liyun Hu, Fan Hong-Yi

By establishing the relation between the optical scaled fractional Fourier transform (FFT) and quantum mechanical squeezing-rotating operator transform, we employ the bipartite entangled state representation of two-mode squeezing operator to extend the scaled FFT to more general cases, such as scaled complex FFT and entangled scaled FFT. The additivity and eigenmodes are presented in quantum version. The relation between the scaled FFT and squeezing-rotating Wigner operator is studied.

Cui-hong Lv, Ya-xin Cai, Yawei Wang