Geometrically protected reversibility in hydrodynamic Loschmidt-echo experiments.

When periodically driven, a number of markedly different systems (colloids, droplets, grains, flux lines) have revealed a transition from a reversible to an irreversible dynamics that hardly depends on the very nature of the interacting objects. Yet, no clear structural signature has been found for this collective self-organization. Here, we demonstrate an archetypal Loschmidt-echo experiment involving thousands of droplets that interact in a reversible fashion via a viscous fluid. First, we show that periodically driven microfluidic emulsions self-organize and geometrically protect their macroscopic reversibility. Self-organization is not merely dynamical: it has a clear structural signature. Second, we show that, above a maximal shaking amplitude, structural order and reversibility are lost simultaneously through a first-order non-equilibrium phase transition. We account for this discontinuous transition in terms of a memory-loss process. Finally, we suggest potential applications of microfluidic echo as a robust tool to tailor colloidal self-assembly at large scales.