  The static and dynamic properties of many-body quantum systems are often well
described by collective excitations, known as quasiparticles. Engineered
quantum systems offer the opportunity to study such emergent phenomena in a
precisely controlled and otherwise inaccessible way. We present a spectroscopic
technique to study artificial quantum matter and use it for characterizing
quasiparticles in a many-body system of trapped atomic ions. Our approach is to
excite combinations of the system's fundamental quasiparticle eigenmodes, given
by delocalised spin waves. By observing the dynamical response to
superpositions of such eigenmodes, we extract the system dispersion relation,
magnetic order, and even detect signatures of quasiparticle interactions. Our
technique is not limited to trapped ions, and it is suitable for verifying
quantum simulators by tuning them into regimes where the collective excitations
have a simple form.
