Measuring correlations in an ensemble of lattice-trapped dipolar atoms*

Understanding the buildup of correlations is an important aspect of studying quantum dynamics.  In a recent theory-experiment collaboration, we perform collective spin measurements to investigate the two-body correlations between a large ensemble of  ultracold chromium atoms frozen in a three dimensional optical lattice. The chromium atoms have spin S=3 and interact via long range and anisotropic dipolar interactions. From measuring the fluctuations of the total magnetization, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. We theoretically analyze the short- and long-time behaviors of the correlations as well as perform numerical simulations for the full time evolution, which are compared with experimental observations to access the quantum nature of the correlations. Our work shows that measuring fluctuations of spin populations provides new ways to characterize correlations in quantum many- body systems, for S> 1/2 spins.