Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states
Richard J. Birrittella, James Schneeloch, Christopher C. Tison, Michael L. Fanto, Paul M. Alsing, Christopher C. Gerry · Physical Review A · 2023
We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e., remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum-mechanical model of nondegenerate second-harmonic generation (SHG) whose evolution is described by the trilinear Hamiltonian of the form ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{\text{shg}}=i\ensuremath{\hbar}\ensuremath{\kappa}(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{-}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}^{\ifmmode\dagger\else\textdagger\fi{}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{c})$. By driving the SHG process with the signal modes of the two down-converters, we show entanglement formation between the generated second-harmonic mode (SH mode) and the noninteracting joint-idler subsystem without the need for any state-reductive measurements on the interacting modes.