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

We provide a quantitative description of the evolution of memory from the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity of each other so that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the emergence of memory in this system, we quantify the storage of energy and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects reduce with increasing particle separation and increase with a skewed stiffness ratio between the traps.