Vacuum entanglement enhancement by a weak gravitational field

Separate regions in space are generally entangled, even in the vacuum state. It is known that this entanglement can be swapped to separated Unruh-DeWitt detectors, i.e., that the vacuum can serve as a source of entanglement. Here, we demonstrate that, in the presence of curvature, the amount of entanglement that Unruh-DeWitt detectors can extract from the vacuum can be increased.

Figure 1

$N^{\prime }=8{\pi }^{2}N/{\alpha }^2$ as a function of $r_1/R_o$. Here $\sigma \Delta E=0.00674$, $R_o\Delta E=1$, and $M/R_o=0.001$. The upper (red) curve corresponds to $L_p/\sigma =1.409$ and the lower (blue) curve to $L_p/\sigma =1.484$. The upper and lower dashed lines are the asymptotes $r_1/R_o\to \infty$. The parameters $\{L_p/\sigma ,\sigma \Delta E,R_o\Delta E\}$ were chosen to display two regimes in which entanglement enhancement and entanglement creation occur, respectively.

Figure 2

$N^{\prime }=8{\pi }^{2}N/{\alpha }^2$ as a function of $\sigma \Delta E$. Here $\Delta E{R}_o=1$, $r_1/R_o=1.1$, and $M/R_o=0.001$. The upper (red) curve corresponds to $L_p/\sigma =1.409$ and the lower (blue) curve to $L_p/\sigma =1.484$. The upper and lower dashed lines are the asymptotes $r_1/R_o\to \infty$.