Quantum Simulation of One-Dimensional Crystal Band Structure with a Tunable Superconducting Electric Circuit

Abstract

This paper presents a concept for a quantum simulator based on a superconducting qubit coupled to a readout resonator, designed to experimentally emulate the band structure of a one-dimensional crystal. The superconducting qubit, with its intrinsic periodic potential from the Josephson effect, serves as a direct analog of an electron in a periodic lattice. The Hamiltonian of the system is analyzed in two complementary regimes: the weak-coupling regime, corresponding to nearly free electrons, and the strong-coupling regime, corresponding to electrons in the tight-binding limit. We show that the system can be continuously swept between these regimes using a flux-tunable symmetric DC-SQUID to vary the effective Josephson energy. To probe the resulting band structure, we propose an experimental method based on two-tone spectroscopy, which maps the qubit's flux-dependent transition spectrum via the dispersive shift of a coupled resonator. Numerical simulations confirm the feasibility of this approach, visualizing the transition from a broad band dispersion in the weak-coupling limit to exponentially narrow bands in the strong-coupling limit. This platform demonstrates how tunable superconducting circuits can be used as versatile quantum simulators for fundamental solid-state physics phenomena.