Analog Superconducting Quantum Simulator for Holstein Polarons

We propose an analog quantum simulator for the Holstein molecular-crystal model based on a dispersive superconducting circuit QED system composed of transmon qubits and microwave resonators. By varying the circuit parameters, one can readily access both the adiabatic and the anti-adiabatic regimes of this model, and realize the coupling strengths required for small-polaron formation. We present a pumping scheme for preparing small-polaron states of arbitrary quasimomentum within time scales much shorter than the qubit decoherence time. The ground state of the system is characterized by anomalous amplitude fluctuation and measurement-based momentum squeezing in the resonator modes.