The spin-boson model involving spins interacting with a bath of quantum harmonic oscillators is a widely used representation of open quantum systems that describe many dissipative processes in physical chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons respectively. We demonstrate a fully programmable method to simulate dissipative dynamics of spin-boson models using a chain of trapped ions where the initial temperature and the spectral densities of the boson bath are engineered by controlling the state of the motional modes and their coupling with qubit states. Our method provides a versatile and precise experimental tool for studying open quantum systems.
