The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundlike mode distinguishes the superfluid from the Bose glass phase. Moreover, spatially resolved spectroscopy provides local spectral properties and allows us to extract the typical spacing of gapless regions, giving a second independent way to uniquely identify all three phases. Our findings have far-ranging implications for a variety of experimental platforms and offer a powerful and versatile probe of the low-energy phases of disordered systems.

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• Quantum quench
• Quasiparticles & collective excitations
• Disordered systems
• Trapped ions
• Ultracold gases
• Matrix product states
• Spectroscopy