  We report the first measurements of the effect of pressure on vibrational
modes in emulsions, which serve as a model for soft frictionless spheres at
zero temperature. As a function of the applied pressure, we find that the
density of states D(omega) exhibits a low-frequency cutoff omega*, which scales
linearly with the number of extra contacts per particle dz. Moreover, for
omega<omega*, D(omega)~ omega^2/omega*^2; a quadratic behavior whose prefactor
is larger than what is expected from Debye theory. This surprising result
agrees with recent theoretical findings. Finally, the degree of localization of
the softest low frequency modes increases with compression, as shown by the
participation ratio as well as their spatial configurations. Overall, our
observations show that emulsions are marginally stable and display
non-plane-wave modes up to vanishing frequencies.
