Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states

Abstract

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 ${\hat{H}}_{\text{shg}}=i\hslash \kappa (\hat{a}\hat{b}{\hat{c}}^{†}-{\hat{a}}^{†}{\hat{b}}^{†}\hat{c})$. 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 non-interacting joint-idler subsystem without the need for any state-reductive measurements on the interacting modes.

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