Entanglement dynamics for atoms near a reflecting boundary: enhancement and suppression by environment-induced interactions

Abstract

We investigate how environment-induced interactions influence the entanglement dynamics of two static atoms placed near a perfectly reflecting boundary. In this setting, the environment-induced interactions include both atom-boundary contributions (position-dependent Lamb shifts) and the induced atom-atom interaction mediated by the field. We show that, regardless of the initial two-atom state, the entanglement dynamics differs qualitatively and quantitatively from predictions that neglect these energy-shift effects. Depending on the geometry and parameter regime, the environment-induced interactions can either enhance entanglement generation -- yielding a larger maximum concurrence and a longer entanglement lifetime -- or suppress it, reducing both the peak concurrence and the survival time. This behavior contrasts sharply with the free-space case, where the environment-induced atom-atom interaction affects entanglement generation only for a restricted class of initial states and does so in an exclusively assisting manner.

Figures (4)

• Figure 1: Two atoms separated by a distance $L$, aligned vertically to the reflecting boundary.
• Figure 2: Time evolution of concurrence for atoms with (black solid line) and without (red dotted line) environment-induced interactions, with only the environment-induced atom--atom interaction (blue dashed line), and with only the environment-induced atom--plate interaction (green dot-dashed line). The parameters are $\omega y=\frac{1}{10},\,\,\omega L=10$ (left), $\omega y =1,\,\,\omega L=10$ (middle), and $\omega y =1,\,\,\omega L=\frac{1}{10}$ (right).
• Figure 3: Maximum concurrence generated during evolution for atoms initially prepared in $|10\rangle$: with (black solid line) and without (red dotted line) environment-induced interactions, with only the environment-induced atom--atom interaction (blue dashed line), and with only the environment-induced atom--plate interaction (green dot-dashed line). The parameters are $\omega y = \frac{1}{10}$ (left) and $\omega y =1$ (right).
• Figure 4: Time evolution of concurrence for atoms with (black solid line) and without (red dotted line) environment-induced interactions, with only the environment-induced atom--atom interaction (blue dashed line), and with only the environment-induced atom--plate interaction (green dot-dashed line). The parameters are $\omega y=\frac{1}{10},\,\,\omega L=19$ (left), $\omega y =1,\,\,\omega L=19$ (middle), and $\omega y =1,\,\,\omega L=1$ (right).