Algorithm for tailoring a quadratic lattice with a local squeezed reservoir to stabilize generic chiral states with nonlocal entanglement

We demonstrate an approach to the generation of custom entangled many-body states through reservoir engineering, using the symmetry properties of bosonic lattice systems coupled to a local squeezed reservoir [Yanay and Clerk, Phys. Rev. A 98, 043615 (2018)]. We outline an algorithm where, beginning with a desired set of squeezing correlations, one uses the symmetry to constrain the Hamiltonian and find a lattice configuration which stabilizes a pure steady state realizing these correlations. We demonstrate how to use this process to stabilize two unique pure states with nonlocal correlations that could be useful for quantum information applications. First, we show how to drive a square lattice into a product state of entangled quadruplets of sites. Second, using a bisected system, we generate a steady state where local measurements in one half of the lattice herald a pure delocalized state in the second half.