LAUSR

Quantum simulators allow to explore static and dynamical properties of otherwise intractable quantum many-body systems. In many instances, however, the read-out limits such quantum simulations. In this work, we introduce an innovative experimental read-out exploiting coherent non-interacting dynamics. Specifically, we present a tomographic recovery method allowing to indirectly measure the second moments of the relative density fluctuations between two one-dimensional superfluids, which until now eluded direct measurements. Applying methods from signal processing, we show that we can reconstruct the relative density fluctuations from non-equilibrium data of the relative phase fluctuations. We employ the method to investigate equilibrium states, the dynamics of phonon occupation numbers and even to predict recurrences. The method opens a new window for quantum simulations with one-dimensional superfluids, enabling a deeper analysis of their equilibration and thermalization dynamics. Quantum simulators give access to quantum dynamics but for large systems it is difficult to read-out informative observables. By using precise modelling the authors demonstrate how to read-out expectation values of non-commuting sets of observables of phonons in cold atomic gases which gives information about their dynamics and thermodynamics.