Reservoir engineering of bosonic lattices using a single local dissipator and chiral symmetry

We show how a generalized kind of chiral symmetry can be used to construct highly-efficient reservoir engineering protocols for bosonic lattices, such as arrays of microwave cavities [arXiv:1710.10318]. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension, and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real space correlation structure in the steady state. We demonstrate the power of the technique using a two-dimensional Hofstadter lattice, which has recently been implemented with superconducting circuits [Owens et al, arXiv:1708.01651].