Multipartite entangled light from driven microcavities

The generation and the characterization of multipartite entangled light is an important and challenging task in quantum optics. In this paper the entanglement properties of the light emitted from a planar semiconductor microcavity are studied. The intracavity scattering dynamics leads to the emission of light that is described by a four-partite $W$ state. Its multipartite correlations are identified by using the method of entanglement witnesses. Entanglement conditions are derived, which are based on a general witness constructed from $W$ states. The results can be used to detect entanglement of light that propagates through lossy and even turbulent media.

Figure 1

Sketch of the considered physical processes. The pumping of the planar microcavity leads to the emission of light whose multipartite entanglement is detected. Inset (a) shows the energy dispersion relations of the excitons, cavity photons, and polaritons. Inset (b) depicts the phase-matching function for $E_{\text{C}}\left(0\right)=E_{\text{X}}=1.5$ eV, ${\Omega }_{\text{R}}=2$ meV, and $\gamma =10\mu$eV. The four pumps with $k_{\text{p}}=0.01k_0$ are arranged on a cone.

Figure 2

Left- and right-hand sides of Eqs. (11) and (13) as functions of $\eta ={\eta }_n$ for $n=1,...,4$. The state ${\rho }_{\text{mix}}$ is partially entangled in regions where $\text{Tr}{\rho }_{\text{mix}}L>f_{\text{full}}\left(L\right)$ and fully entangled if $\text{Tr}{\rho }_{\text{mix}}L>f_{\text{part}}\left(L\right)$ with respect to the choice $L={\rho }_{\text{mix}}$.

Figure 3

Contour plots of (a) $\text{Tr}{\rho }_{\text{mix}}L-f_{\text{full}}\left(L\right)$ and (b) $\text{Tr}{\rho }_{\text{mix}}L-f_{\text{part}}\left(L\right)$ as functions of $\eta ={\eta }_1={\eta }_2={\eta }_3$ and ${\eta }^{\prime }={\eta }_4$. The state ${\rho }_{\text{mix}}$ is partially or fully entangled in regions where the respective function takes positive values.