can be described by a Bose-Hubbard
Hamiltonian with attractive interactions for polaritons, superpositions of
photons and qubit excitations. This setup we envisage constitutes one of the
first platforms where all technological components that are needed to
experimentally study chains of strongly interacting polaritons have already
been realized. By driving the first stripline resonator with a microwave source
and detecting the output field of the last stripline resonator one can
spectroscopically probe properties of the system in the driven dissipative
regime. We calculate the stationary polariton density and density-density
correlations $g^{(2)}$ for the last cavity which can be measured via the output
field. Our results display a transition from a coherent to a quantum field as
the ratio of on site interactions to driving strength is increased.

# Bose-Hubbard dynamics of polaritons in a chain of circuit QED cavities

We investigate a chain of superconducting stripline resonators, each
interacting with a transmon qubit, that are capacitively coupled in a row. We
show that the dynamics of this system