  Atomic clusters presents an isolated system that models the bulk materials
whose mechanism of HHG remains uncertain, and a promising medium to produce HHG
beyond the limited conversion efficiency for gaseous atoms. Here we reveal that
the oscillation of collective electron motion within clusters develops after
the interaction of intense laser fields, and it significantly enhances the
harmonic dipole and increases the quantum phase of the harmonics.
Experimentally, the phase matching conditions of HHG from nanometer xenon
clusters and atoms are distinguished, which confirms the enhanced internal
field that was proposed theoretically a decade ago. The separation of HHG from
atoms and clusters allows the determination of the amplitude of the HHG for
clusters to be 5 orders higher, corresponding to 4 times higher conversion
efficiency for atomic response. The finding provides an insight on the HHG
mechanism of bulk materials and a means by which an efficient coherent X-ray
source can be developed.
