Entanglement for excitons in two quantum dots placed in two separate single-mode cavities

The dynamical behavior of entanglement for excitons in two quantum dots placed in two separately single-mode optical cavities driven by an external broadband two-mode squeezed vacuum is studied in the low exciton density regime. It is found that if the field in the two separate cavities is initially prepared in a pure two-mode squeezed vacuum state, the excitons in the two quantum dots can evolve into a pure entangled state only when the dissipation of the cavities and exciton modes is negligible. When the effect of the dissipation is included, the excitons will be in a two-mode Gaussian entangled mixed state whose properties are decided by the externally driven field and the initial field. The dependence of the entanglement property of the excitons in the two quantum dots on the squeezing properties of the fields in the two cavities is also discussed.

Figure 1

The linear entropy $S$ versus $gt$ for different relative phase $\theta -\varphi$, in which $\gamma =\kappa =0.1\mathrm{g}$, $N=3$, $M=2\sqrt{3}$, $r=0.8$, and $\theta -\varphi =\pi$ (solid), $\pi ∕2$ (dashed), and 0 (dotted).

Figure 2

The negativity ${\lambda }_{-}$ versus $gt$ for different relative phase $\theta -\varphi$, in which $\kappa =\gamma =0.1\mathrm{g}$, $N=3$, $M=2\sqrt{3}$, $r=0.8$, and $\theta -\varphi =\pi$ (solid), $\pi ∕2$ (dashed), and 0 (dotted). The inset plots the time evolution of the exciton number $n$.

Figure 3

The negativity ${\lambda }_{-}$ versus $gt$ for different $\kappa$, here $\theta -\varphi =\pi$, $\gamma =0.1\mathrm{g}$, $N=3$, $M=2\sqrt{3}$, $r=0.8$, and $\kappa =0.02\mathrm{g}$ (solid), $\kappa =0.1\mathrm{g}$(dotted), and $\kappa =0.5\mathrm{g}$ (dashed). The exciton number $n$ is plotted in the inset.