On the entangled fractional squeezing transformation (Englisch)

Abstract We propose an entangled fractional squeezing transformation (EFrST) generated by using two mutually conjugate entangled state representations with the following operator: $$e^{ - i\alpha \left( {a_1^\dag a_2^\dag + a_1 a_2 } \right)} e^{i\pi a_2^\dag a_2 }$$; this transformation sharply contrasts the complex fractional Fourier transformation produced by using $$e^{ - i\alpha \left( {a_1^\dag a_1 + a_2^\dag a_2 } \right)} e^{i\pi a_2^\dag a_2 }$$ (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., tanα → tanhα and sinα → sinh α. The fractional property of the EFrST can be well described by virtue of the properties of the entangled state representations.