  Quantum systems lose coherence upon interaction with the environment and tend
towards classical states. Quantum coherence is known to exponentially decay in
time so that macroscopic quantum superpositions are generally unsustainable. In
this work, slower than exponential decay of coherences is experimentally
realized in an atom-optics kicked rotor system subjected to non-stationary
L\'{e}vy noise in the applied kick sequence. The slower coherence decay
manifests in the form of quantum subdiffusion that can be controlled through
the L\'{e}vy exponent. The experimental results are in good agreement with the
analytical estimates and numerical simulations for the mean energy growth and
momentum profiles of atom-optics kicked rotor.
