  Giant atoms provide a promising platform for engineering decoherence-free
interactions which is a major task in modern quantum technologies. Here we
study systematically how to implement complex decoherence-free interactions
among giant atoms resorting to periodic coupling modulations and suitable
arrangements of coupling points. We demonstrate that the phase of the
modulation, which is tunable in experiments, can be encoded into the
decoherence-free interactions, and thus enables phase-dependent dynamics when
the giant atoms constitute an effective closed loop. Moreover, we consider the
influence of non-Markovian retardation effect arising from large separations of
the coupling points and study its dependence on the modulation parameters.
