  The dependence of the light and charge yield of liquid xenon on the applied
electric field and recoil energy is important for dark matter detectors using
liquid xenon time projections chambers. Few measurements have been made of this
field dependence at recoil energies less than 10 keV. In this paper we present
results of such measurements using a specialized detector. Recoil energies are
determined via the Compton coincidence technique at four drift fields relevant
for liquid xenon dark matter detectors: 0.19, 0.48, 1.02, and 2.32 kV/cm. Mean
recoil energies down to 1 keV were measured with unprecedented precision. We
find that the charge and light yield are anti-correlated above 3 keV, and that
the field dependence becomes negligible below 6 keV. However, below 3 keV we
find a charge yield significantly higher than expectation and a reconstructed
energy deviating from linearity.
