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.

量子模拟器可以探索原本难以处理的量子多体系统的静态和动态特性。但是，在许多情况下，读数限制了这种量子模拟。在这项工作中，我们介绍了利用相干非相互作用动力学的创新性实验性读数。具体而言，我们提出了一种层析成像恢复方法，该方法可以间接测量两个一维超流体之间的相对密度波动的第二阶矩，直到现在仍无法进​​行直接测量。应用信号处理方法，我们可以从相对相位波动的非平衡数据中重建相对密度波动。我们采用这种方法来研究平衡状态，声子职业数的动态，甚至预测复发。