Unraveling the excitation spectrum of many-body systems from quantum quenches

Quenches are now routinely used in synthetic quantum systems to study a variety of fundamental effects, including ergodicity breaking, light-cone-like spreading of information, and dynamical phase transitions. It was shown recently that the dynamics of equal-time correlators may be related to ground-state phase transitions and some properties of the system excitations. Here, we show that the full low-lying excitation spectrum of a generic many-body quantum system can be extracted from the after-quench dynamics of equal-time correlators. We demonstrate it for a variety of one-dimensional lattice models amenable to exact numerical calculations, including Bose and spin models, with short-or long-range interactions. The approach also applies to higher dimensions, correlated fermions, and continuous models. We argue that it provides an alternative approach to standard pump-probe spectroscopic methods and discuss its advantages.