  Motivated by the dynamics of particles embedded in active gels, both in-vitro
and inside the cytoskeleton of living cells, we study an active generalization
of the classical trap model. We demonstrate that activity leads to dramatic
modifications in the diffusion compared to the thermal case: the mean square
displacement becomes sub-diffusive, spreading as a power-law in time, when the
trap depth distribution is a Gaussian and is slower than any power-law when it
is drawn from an exponential distribution. The results are derived for a
simple, exactly solvable, case of harmonic traps. We then argue that the
results are robust for more realistic trap shapes when the activity is strong.
