Stationary discrete solitons in circuit QED
  We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions, by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain. 
Uta Naether, Fernando Quijandr\'ia, Juan Jos\'e Garc\'ia-Ripoll, and   David Zueco
quant-ph cond-mat.mes-hall cond-mat.supr-con nlin.PS