Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

We study the problem of rapid change of the interaction parameter (quench) in many-body low-dimensional system. It is shown that, measuring correlation functions after the quench the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for non-integrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring power spectrum in dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as experimental test of our predictions.