Distributing fully optomechanical quantum correlations

We present a scheme to prepare quantum correlated states of two mechanical systems based on the pouring of preavailable all-optical entanglement into the state of two micromirrors belonging to remote and noninteracting optomechanical cavities. We show that, under realistic experimental conditions, the protocol allows for the preparation of a genuine quantum state of a composite mesoscopic system whose nonclassical features extend beyond the occurrence of entanglement. We finally discuss a way to access such mechanical correlations.

Figure 1

Sketch of the thought experiment: two optomechanical cavities are pumped by classical laser fields (not shown) and two-mode squeezed light, generated by feeding of a nonlinear crystal. We show the symbols for polarization beam splitters (PBSs) and quarter-wave plates (QWPs) that are used to direct the polarized input squeezed light (output field) to the cavity (the homodyne-detection stage).

Figure 2

Logaritmic negativity against the effective detuning $\Delta$ and the dimensionless squeezing parameter $r$ for $T=2\hspace{0.5em}\mathrm{mK}$. The remaining set of parameters is borrowed from the recent experiment reported in Ref. [7].

Figure 3

(a) Logaritmic negativity against the dimensionless squeezing parameter $r$ and the temperature of the mechanical bath $T$ (in kelvins) for $\Delta ={\omega }_m$. (b) Gaussian quantum discord against squeezing and temperature for $\Delta ={\omega }_m$. Nonclassicality of the mechanical modes is found up to $T=0.12\mathrm{\hspace{0.5em}}\mathrm{K}$.

Figure 4

Entanglement input-output relation showing the mapping of the mechanical entanglement onto the optical entanglement shared by the auxiliary modes. Quantities on the horizontal and vertical axes are dimensionless.