Single-Mode Photon-Addition for the Two-Mode Squeezed State and its Statistical Properties

Abstract

We construct a new optical field, denoted as $\rho _{0}\equiv \left \vert \psi \right \rangle _{ll}\left \langle \psi \right \vert $ , $\left \vert \psi \right \rangle _{l}=\frac {\text {sech}^{l}\lambda }{\sqrt {l!} }b^{\dagger l}S_{2}\left \vert 00\right \rangle $ , by adding single-mode l-photon to a two-mode squeezed vacuum state, where $S_{2}=\exp \left [ \lambda \left (a^{\dagger }b^{\dagger }-ab\right ) \right ] $ is the two-mode squeezing operator. We find that its partial trace over b-mode will lead to a negative-binomial optical field in a-mode characteristic of l, which exhibits quantum entanglement. The photon number fluctuation of the new optical field both in a-mode and in b-mode is investigated. We employ the summation method within ordered product of operators to proceed our discussion.