On the entangled fractional squeezing transformation

Abstract

We propose an entangled fractional squeezing transformation (EFrST) generated by using two mutually conjugate entangled state representations with the following operator: {\mathrm{e}}^{-\mathrm{i}\alpha (a_{\mathrm{1}}^{†}{a}_{\mathrm{2}}^{†}+a_{\mathrm{1}}{a}_{\mathrm{2}})}{\mathrm{e}}^{\mathrm{i}\pi a_{\mathrm{2}}^{†}{a}_{\mathrm{2}}}; this transformation sharply contrasts the complex fractional Fourier transformation produced by using {\mathrm{e}}^{-\mathrm{i}\alpha (a_{\mathrm{1}}^{†}{a}_{\mathrm{2}}^{†}+a_{\mathrm{2}}^{†}{a}_{\mathrm{2}})}{\mathrm{e}}^{\mathrm{i}\pi a_{\mathrm{2}}^{†}{a}_{\mathrm{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 → sinhα. The fractional property of the EFrST can be well described by virtue of the properties of the entangled state representations.

Keywords

entangled fractional squeezing transformation / entangled state representation / squeezing operator / core operator

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Higher Education Press and Springer-Verlag Berlin Heidelberg