  We show experimentally and theoretically that the spectral components of a
multi-octave frequency comb spontaneously created by stimulated Raman
scattering in a hydrogen-filled hollow-core photonic crystal fiber exhibit
strong self coherence and mutual coherence within each 12 ns driving laser
pulse. This coherence arises in spite of the field's initiation being from
quantum zero-point fluctuations, which causes each spectral component to show
large phase and energy fluctuations. This points to the possibility of an
optical frequency comb with nonclassical correlations between all comb lines.
