  We demonstrate sub-Doppler laser cooling of $ ^{39} $K using degenerate Raman
sideband cooling via the 4S$_{1/2} \rightarrow $5P$ _{1/2} $ transition at
404.8 nm. By using an optical lattice in combination with a magnetic field and
optical pumping beams, we obtain a spin-polarized sample of up to $5.6 \times
10^{7}$ atoms cooled down to a sub-Doppler temperature of 4 $\mu $K, reaching a
peak density of $3.9 \times 10^{9}$ atoms/cm$ ^{3} $, a phase-space density
greater than $ 10^{-5} $, and an average vibrational level of $ \langle \nu
\rangle=0.6 $ in the lattice. This work opens up the possibility of
implementing a single-site imaging scheme in a far-detuned optical lattice
utilizing shorter wavelength transitions in alkali atoms, thus allowing
improved spatial resolution.
