  We have fabricated and studied a system of two tunable and coupled nonlinear
superconducting resonators. The nonlinearity is introduced by galvanically
coupled dc-SQUIDs. We simulate the system response by means of a circuit model,
which includes an additional signal path introduced by the electromagnetic
environment. Furthermore, we present two methods allowing us to experimentally
determine the nonlinearity. First, we fit the measured frequency and flux
dependence of the transmission data to simulations based on the equivalent
circuit model. Second, we fit the power dependence of the transmission data to
a model that is predicted by the nonlinear equation of motion describing the
system. Our results show that we are able to tune the nonlinearity of the
resonators by almost two orders of magnitude via an external coil and two
on-chip antennas. The studied system represents the basic building block for
larger systems, allowing for quantum simulations of bosonic many-body systems
with a larger number of lattice sites.
