  In this work, we propose and study a double Kondo lattice model which hosts
robust superconductivity. The system consists of two identical Kondo lattice
model, each with Kondo coupling $J_K$ within each layer, while the localized
spin moments are coupled together via an inter-layer on-site antiferromagnetic
spin coupling $J_\perp$. We consider the strong $J_\perp$ limit, wherein the
local moments tend to form rung singlets and are thus gapped. However, the
Kondo coupling $J_K$ transmits the inter-layer entanglement between the local
moments to the itinerant electrons. Consequently, the itinerant electrons
experience a strong inter-layer antiferromangetic spin coupling and form strong
inter-layer pairing, which is confirmed through numerical simulation in one
dimensional system. Experimentally, the $J_K \rightarrow -\infty$ limits of the
model describes the recently found bilayer nickelate La$_3$Ni$_2$O$_7$, while
the $J_K>0$ side can be realized in tetralayer optical lattice of cold atoms.
Two extreme limits, $J_K \rightarrow -\infty$ and $J_K \rightarrow +\infty$
limit are shown to be simplified to a bilayer type II t-J model and a bilayer
one-orbital t-J model, respectively. Thus, our double Kondo lattice model
offers a unified framework for nickelate superconductor and tetralayer optical
lattice quantum simulator upon changing the sign of $J_K$. We highlight both
the qualitative similarity and the quantitative difference in the two sides of
$J_K$. Finally, we discuss the possibility of a symmetric Kondo breakdown
transition in the model with a symmetric pseudogap metal corresponding to the
usual heavy Fermi liquid.
