Following the laser cooling proposals, in 1978 two research groups that Wineland, Drullinger and Walls of NIST, and Neuhauser, Hohenstatt, Toscheck and Dehmelt of the University of Washington succeeded in laser cooling atoms. The NIST group wanted to reduce the effect of Doppler broadening on spectroscopy. They cooled magnesium ions in a Penning trap to < 40 Kelvin.  The Washington group cooled barium ions. 
The research from both groups served to illustrate the mechanical properties of light. Around this time, laser cooling techniques had allowed for temperatures lowered to around 40 kelvins.
Influenced by the Wineland's work on laser cooling ions, William Phillips applied the same principles to laser cool neutral atoms. In 1982, he published the first paper where neutral atoms were laser cooled. The process used is now known as the Zeeman slower and is a standard technique for slowing an atomic beam.