A quantitative analysis of memory effects in the viscously coupled dynamics of optically trapped Brownian particles

We provide a quantitative description of the memory effects existing in the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity to each other such 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 memory effects, we quantify the storage of energy in terms of various system parameters 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 are maximized at a certain trap stiffness ratio, and reduce with increasing particle separation. The technique can be generally used to determine the effective viscoelastic parameters of any such fluid-particle systems, and can thus help understand the interactions between active particles mediated by simple or complex fluids.