  We show how experimentally available bilayer lattice systems can be used to
prepare quantum many-body states with exceptionally low entropy in one layer,
by dynamically disentangling the two layers. This disentangling operation moves
one layer - subsystem $A$ - into a regime where excitations in $A$ develop a
single-particle gap. As a result, this operation maps directly to cooling for
subsystem $A$, with entropy being shuttled to the other layer. For both bosonic
and fermionic atoms, we study the dynamics of this process, and show that
disentangling can be realised cleanly in ongoing optical lattice experiments.
The corresponding entanglement entropies are directly measurable with quantum
gas microscopes, and as a tool for producing lower-entropy states, this
technique opens a range of applications beginning with simplifying production
of anti-ferromagnetically ordered states of fermions.
