Transfer and preservation of entanglement in a hybrid optomechanical system

We propose a scheme for entangling a movable mirror and two atomic ensembles in a coupled hybrid optomechanical system. Using the logarithmic negativity for the entanglement measure, we analyze the effect of the coupling strength between the two cavities on the entanglement of the movable mirror and the atomic ensembles, and we analyze the effect of the atom-cavity coupling constant on the entanglement of the movable mirror and the atomic ensembles. It is found that the entanglements of the movable mirror with one atomic ensemble transfer to the movable mirror with another atomic ensemble, and the robustness of the entanglement is enhanced by the coupling between the two cavities. The entanglements between the movable mirror and atomic ensembles are enhanced together with atom-cavity coupling increasing, and the entanglements have maxima in the accessibly parameters regime of the atom-cavity coupling constant.

Figure 1

Schematic diagram of the hybrid optomechanical system.

Figure 2

(a) Logarithmic negativity of entanglement between the movable mirror and the other subsystems as a function of the coupling strength $J$. (b) Steady-state mean value $\left|a_{1s}\right|(\left|a_{2s}\right|,G)$ as a function of the coupling strength $J$.

Figure 3

The logarithmic negativity of the entanglement between atomic ensemble II and the oscillator (a) as a function of the detuning $\mathrm{\Delta }$ at a temperature of $T=0.4$ K and (c) as a function of the environment temperature $T$ at $\mathrm{\Delta }=\text{0}\text{.6}{\omega }_m$. The contour plots (b) and (d) correspond to panels (a) and (c) with continuous change of the $J$.

Figure 4

The logarithmic negativity of the entanglement between the movable mirror and atomic ensemble I: (a) as a function of detuning $\mathrm{\Delta }$, at the environment temperature $T=0.4$ K, and (b) as a function of the environment temperature $T$ at $\mathrm{\Delta }=\text{0}\text{.6}{\omega }_m$. The contour plots (b) and (d) correspond to panels (a) and (c) with continuous change of $J$.

Figure 5

The logarithmic negativity $E_{Nma1}$ and $E_{Nma2}$ versus the detuning $\mathrm{\Delta }/{\omega }_{\text{m}}$ with different coupling strengths $g$: (a) $E_{Nma1}$ and (c) $E_{Nma2}$. The contour plots (b) and (d) of $E_{Nma1}$ and $E_{Nma2}$ with continuous change of the coupling strength $g$.