  We analyze a method for preparing low-entropy many-body states in isolated
quantum optical systems of atoms, ions and molecules. Our approach is based
upon shifting entropy between different regions of a system by spatially
modulating the magnitude of the effective Hamiltonian. We conduct two case
studies, on a topological spin chain and the spinful fermionic Hubbard model,
focusing on the key question: can a "conformal cooling quench" remove
sufficient entropy within experimentally accessible timescales? Finite
temperature, time-dependent matrix product state calculations reveal that even
moderately sized "bath" regions can remove enough energy and entropy density to
expose coherent low temperature physics. The protocol is particularly natural
in systems with long-range interactions such lattice-trapped polar molecules
and Rydberg dressed atoms where the magnitude of the Hamiltonian scales
directly with the density. To this end, we propose a simple implementation of
conformal cooling quenches in a dilutely-filled optical lattice, where
signatures of quantum magnetism can be observed.
