  The dynamics of chaotic Hamiltonian systems such as the kicked rotor
continues to guide our understanding of transport and localization processes.
The localized states of the quantum kicked rotor decay due to decoherence
effects if subjected to stationary noise. The associated quantum diffusion
increases monotonically as a function of a parameter characterising the noise
distribution. In this work, for the Levy kicked atom-optics rotor, it is
experimentally shown that by tuning a parameter characterizing the Levy
distribution, quantum diffusion displays non-monotonic behaviour. The
parameters for optimal diffusion rates are analytically obtained and they
reveal a good agreement with the cold atom experiments and numerics. The
non-monotonicity is shown to be a quantum effect that vanishes in the classical
limit.
