Extracting spectral properties of small Holstein polarons from a transmon-based analog quantum simulator

Abstract: The Holstein model, which describes purely local coupling of an itinerant excitation (electron, hole, exciton) with zero-dimensional (dispersionless) phonons, represents the paradigm for short-range excitation-phonon interactions. It is demonstrated here how spectral properties of small Holstein polarons -- heavily phonon-dressed quasiparticles, formed in the strong-coupling regime of the Holstein model -- can be extracted from an analog quantum simulator of this model. This simulator, which is meant to operate in the dispersive regime of circuit quantum electrodynamics, has the form of an array of capacitively coupled superconducting transmon qubits and microwave resonators, the latter being subject to a weak external driving. The magnitude of $XY$-type coupling between adjacent qubits in this system can be tuned through an external flux threading the SQUID loops between those qubits; this translates into an {\em in-situ} flux-tunable hopping amplitude of a fictitious itinerant spinless-fermion excitation, allowing one to access all the relevant physical regimes of the Holstein model. By employing the kernel-polynomial method, based on expanding dynamical response functions in Chebyshev polynomials of the first kind and their recurrence relation, the relevant single-particle momentum-frequency resolved spectral function of this system is computed here for a broad range of parameter values. To complement the evaluation of the spectral function, it is also explained how -- by making use of the many-body version of the Ramsey interference protocol -- this dynamical-response function can be measured in the envisioned analog simulator.