  We present new measurements of the scintillation and ionization yields in
liquid xenon for low energy electronic (about 3--7 keV$_{ee}$) and nuclear
recoils (about 8--20 keV$_{nr}$) at different drift fields from 236 V/cm to
3.93 kV/cm, using a three-dimensional sensitive liquid xenon time projection
chamber with high energy and position resolutions. Our measurement of signal
responses to nuclear recoils agrees with predictions from the NEST model.
However, our measured ionization (scintillation) yields for electronic recoils
are consistently higher (lower) than those from the NEST model by about 5
e$^-$/keV$_{ee}$ (ph/keV$_{ee}$) at all scanned drift fields. New recombination
parameters based on the Thomas-Imel box model are derived from our data. Given
the lack of precise measurement of scintillation and ionization yields for low
energy electronic recoils in liquid xenon previously, our new measurement
provides so far the best available data covering low energy region at different
drift fields for liquid xenon detectors relevant to dark matter searches.
