This paper introduces a novel experimental read-out method for quantum simulators, leveraging coherent non-interacting dynamics to indirectly measure second moments of relative density fluctuations between two one-dimensional superfluids. The method uses a tomographic recovery technique, reconstructing relative density fluctuations from non-equilibrium data of relative phase fluctuations. It's applied to investigate equilibrium states, phonon occupation number dynamics, and recurrence prediction, opening new avenues for analyzing equilibration and thermalization dynamics in 1D superfluids.

M. Gluza, T. Schweigler, B. Rauer, C. Krumnow, J. Schmiedmayer, J. Eisert