Detection of out-of-time-order correlators and information scrambling in cold atoms: Ladder-XX model

Out-of-time-order correlators (OTOC), recently being the center of discussion on quantum chaos, are a tool to understand the information scrambling in different phases of quantum many-body systems. We propose a disordered ladder spin model, XX-ladder, which can be designed in a scalable cold atom setup to detect OTOC with a novel sign reversal protocol for the evolution backward in time. We study both the clean and disordered limits of XX-ladder and characterize different phases (ergodic-MBL) of the model based on the decay properties of OTOCs. Emergent effective lightcone shows sublinear behaviour, while the butterfly cones drastically differ from the lightcone via demonstrating superlinear behaviour. Based on our results, one can observe how the information scrambling changes in the transition from well-studied 1D spin models to unexplored 2D spin models in a local setting.