  We consider a typical class of systems with delayed nonlinearity, which we
show to exhibit chaotic diffusion. It is demonstrated that a periodic
modulation of the time-lag can lead to an enhancement of the diffusion constant
by several orders of magnitude. This effect is the largest if the circle map
defined by the modulation shows mode locking and more specifically, fulfills
the conditions for laminar chaos. Thus we establish for the first time a
connection between Arnold tongue structures in parameter space and diffusive
properties of a delay system. Counterintuitively, the enhancement of diffusion
is accompanied by a strong reduction of the effective dimensionality of the
system.
