  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.

Soft Condensed Matter