Gray molasses cooling of $^{39}$K to a high phase-space density

We present new techniques in cooling 39K atoms using laser light close to the D1 transition. First, a new compressed-MOT configuration is taking advantage of gray molasses type cooling induced by blue-detuned D1 light. It yields an optimized density of atoms. Then, we use pure D1 gray molasses to further cool the atoms to an ultra-low temperature of 6\,$\mu$K. The resulting phase-space density is $2 \times 10^{-4}$ and will ease future experiments with ultracold potassium. As an example, we use it to directly load up to $3\times 10^7$ atoms in a far detuned optical trap, a result that opens the way to the all-optical production of potassium degenerate gases.