Spectral features of polaronic excitations in a superconducting analog simulator

We investigate spectral properties of polaronic excitations within the framework of an analog quantum simulator based on inductively coupled superconducting qubits and microwave resonators. This system emulates a lattice model that describes a nonlocal coupling of an itinerant spinless-fermion excitation to dispersionless phonons. The model is characterized by a sharp, level-crossing transition for a critical value of the effective excitation-phonon coupling strength; above the transition point, the ground state of this model corresponds to a heavily-dressed excitation (small polaron). Using the kernel-polynomial method, based on an expansion in Chebyshev polynomials of the first kind, we evaluate the momentum-frequency resolved spectral function of this system for a broad range of frequencies at several different quasimomenta. To make contact with experiments, we establish a link with a method for extracting dynamical-response functions in systems with local (single-qubit) addressability, which is based on a generalized (multi-qubit) version of the Ramsey interference protocol.