  We show that the non-local polarization response in a multimode circuit-QED
setup, devised from a Cooper pair box coupled to a long chain of Josephson
junctions, provides an alternative route to access the elusive Kondo screening
cloud. For moderate circuit impedance, we compute analytically the universal
lineshape for the decay of the charge susceptibility along the circuit, that
relates to spatial entanglement between the qubit and its electromagnetic
environment. At large circuit impedance, we numerically find further spatial
correlations that are specific to a true many-body state.
