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Quantum walk research has mainly focused on evolutions due to repeatedapplications of time-independent unitary coin operators. However, the idea ofcontrolling the single particle evolution using time-dependent unitary coinshas still been a subject of multiple studies as it not only hosts interestingpossibilities for quantum information processing but also opens a much richerarray of phenomena including static and dynamic localizations. So far, suchstudies have been performed only for single quantum walkers. In case ofmulti-walker systems, time-dependent coins may generate measurable phenomenanot described by the single-particle model, due to entanglement and interactionamong the walkers. In this context, we present here a thorough numerical studyof an one dimensional system of two quantum walkers exhibiting rich collectivedynamics controlled by simple time-dependent unitary coins proposed in [Phys.Rev. A \textbf{80}, 042332(2009)] and [Phys. Rev. A \textbf{73},062304(2006)].We study how the interplay of coin time-dependence, simple interaction schemes,entanglement and the relative phase between the coin states of the particlesinfluences the evolution of the quantum walk. The results show that the systemoffers a rich variety of collective dynamical behavior while being controlledby time dependent coins. In particular, we find and characterize fascinatingtwo-body localization phenomena with tunable quasiperiodic dynamics ofcorrelations and entanglements which are quantities of quantum origin.

Diverse tunable dynamics of two quantum random walkers