Two-mode light states before and after delocalized single-photon addition

Abstract

We studied the effect of delocalized single-photon addition (DPA ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}^{\ifmmode\dagger\else\textdagger\fi{}}+{e}^{i\ensuremath{\varphi}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}^{\ifmmode\dagger\else\textdagger\fi{}}$) on two input modes containing four cases: two independent coherent states (CSs), two independent thermal states (TSs), two independent single-mode squeezed vacuums (SVs), and an entangled two-mode squeezed vacuum (TMSV). In essence, four types of non-Gaussian entangled light states are generated. We studied three different resources (including entanglement, discorrelation, and Wigner negativity) for each two-mode light state. The output states after DPA are entangled, with more parameters and complex structures, characterizing more Wigner negativity or even discorrelation. In contrast, the CSs case is the most tunable protocol, because its negativity under partial transposition, discorrelation, and Wigner logarithmic negativity are more sensitive to superposition phase $\ensuremath{\varphi}$ than those in TSs, SVs, and TMSV cases.