Figure 1

A pair of independent arrays of linearly coupled quantum systems is locally driven by a two-mode entangled field. The elements in each array are labeled by the indices $j\in [1,N]$ (first chain) and $j\in [N+1,2N]$ (second chain). The steady-state inter-array entangled pairs are marked by dashed arrows.Reuse & Permissions

Figure 2

$E_N^{(\mathrm{cav})}$ as a function of (a) the pair-site label ($j$, $N+j$) (with $N=20$ and ${\kappa }_j\equiv {\kappa }_0$ $\forall j$), (b) $N$ (with ${\kappa }_j=0.1\eta$, $\forall j$), (c) $\overline{n}$ [with $\overline{m}=\sqrt{\overline{n}(\overline{n}+1)}$], (d) $\overline{m}$ (with $\overline{n}=1$), and (e) ${\kappa }_N={\kappa }_{2N}$ (with ${\kappa }_{j\ne N,2N}=0$). In all cases, ${\eta }_j=\eta$, $\forall j$, and $\zeta =\eta$. The remaining parameters in (a), (b), and (e) are $\overline{n}=1$ and $\overline{m}=\sqrt{\overline{n}(\overline{n}+1)}$; in (c) and (d), they are ${\kappa }_j=0.1\eta$ and $N=10$. The insets indicate the pair ($j$, $N+j$) corresponding to each line. In (e), the dash-dotted curve corresponds to all pairs ($j$, $N+j$) for $j\in [2,N-1]$. These results are independent of $N$ and have been verified numerically for arrays of size up to $N=30$. The solid thick (gray) lines report the entanglement of the driving field that is equal to the entanglement of each pair when ${\kappa }_j=0$, $\forall j$.Reuse & Permissions

Figure 3

(a) $E_N^{\mathrm{cav}}$ for a model with random couplings as specified in the text. The curves are obtained by averaging the result over 500 realizations. For each value of $\Delta \xi$, the vertical bars represent the interval between the realizations of maximum and minimum entanglement. The other parameters are $N=10$, $\overline{n}=1$, $\overline{m}=\sqrt{\overline{n}(\overline{n}+1)}$, $\zeta ={\eta }_0$, and ${\kappa }_j=0.02{\eta }_0$ $\forall j$. (b), (c) Comparison between the logarithmic negativity for atoms in cavity arrays, (b) $E_N^{(\mathrm{at})}$, and for spins in $XX$ spin chains, (c) $E_N^{(\mathrm{spins})}$, as functions of $\overline{m}$ for $\overline{n}=1$. The remaining parameters are ${\kappa }_j=0$ $\forall j$, $N=3$, $\zeta =\eta$, and $g=0.01\eta$ for the atoms and $N=3$, and $J_j=\gamma$ $\forall j$ for the spins. The insets specify the correspondence between curves and pairs ($j$, $j+N$).Reuse & Permissions