  Clusters and nanodroplets hold the promise of enhancing high-order nonlinear
optical effects due to their high local density. However, only moderate
enhancement has been demonstrated to date. Here, we report the observation of
energetic electrons generated by above-threshold ionization (ATI) of helium
(He) nanodroplets which are resonantly excited by ultrashort extreme
ultraviolet (XUV) free-electron laser pulses and subsequently ionized by
near-infrared (NIR) or near-ultraviolet (UV) pulses. The electron emission due
to high-order ATI is enhanced by several orders of magnitude compared to He
atoms. The crucial dependence of the ATI intensities with the number of
excitations in the droplets suggests a local collective enhancement effect.
