  We propose an analog quantum simulator for the Holstein molecular-crystal
model based on a superconducting circuit QED system in the dispersive regime.
By varying the driving field on the superconducting resonators, one can readily
access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph
coupling required for small-polaron formation can also be reached. We show that
small-polaron state of arbitrary quasimomentum can be generated by applying a
microwave pulse to the resonators. We also show that significant squeezing in
the resonator modes can be achieved in the polaron-crossover regime through a
measurement-based scheme.
