Detection of out-of-time-order correlators and information scrambling in cold atoms

We propose a disordered ladder spin model which can be designed in a scalable cold atom setup at the hard-core boson limit to dynamically detect out-of-time order correlators (OTOC) and hence information scrambling. Our protocol utilizes the Hamiltonian sign reversal for the evolution backward in time by applying single spin gates successively. We study different limits of disordered Ladder-XY model with focusing on its OTOC behavior and level statistics. We show that in its chaotic limit, disordered ladder-XY model decays exponentially in early-time with power-law tails before its scrambling time and it demonstrates a range of lightcones due to local spin-spin interactions. Based on our results, one can observe how the ladder systems could be useful to understand and experiment information scrambling in the transition from well-studied 1D models to unexplored 2D models.