Proposal for the experimental detection of many-body quantum chaos via dynamics

Recently, there has been a resurgence of interest in quantum chaos, especially when caused by interactions between particles. A common diagnostic tool of quantum chaos is the presence of correlated eigenvalues and level statistics comparable to those of random matrices. However, the spectrum is not easily accessible to current experiments with cold atoms and ion traps, which are designed to investigate many-body quantum dynamics. For these experiments, we propose a way to detect many-body quantum chaos directly through the dynamics. We show that the spectral correlations are manifested in the form a the dip-ramp-plateau structure (aka correlation hole) in two exerimental quantities, the survival probability (dynamical version of the spectral form factor) and the spin autocorrelation function (density imbalance). Our results suggest that observation of this structure is within reach of current experimental capabilities.