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We provide a quantitative description of the evolution of memory from theapparently random Markovian dynamics of a pair of optically trapped colloidalmicroparticles in water. The particles are trapped in very close proximity ofeach other so that the resultant hydrodynamic interactions lead tonon-Markovian signatures manifested by the double exponential auto-correlationfunction for the Brownian motion of each particle. In connection with theemergence of memory in this system, we quantify the storage of energy anddemonstrate that a pair of Markovian particles - confined in individual opticaltraps in a viscous fluid - can be described in the framework of a singleBrownian particle in a viscoelastic medium. We define and quantify theequivalent storage and loss moduli of the two-particle system, and showexperimentally that the memory effects reduce with increasing particleseparation and increase with a skewed stiffness ratio between the traps.

A quantitative analysis of the emergence of memory in the viscously coupled dynamics of colloids