We report the measurement of longitudinal electron diffusion coefficients in liquid argon for electric fields between 100 and 2000 V/cm with a gold photocathode as a bright electron source. The measurement principle, apparatus, and data analysis are described. Our results, which are consistent with previous measurements in the region between 100 to 350 V/cm [1] , are systematically higher than the prediction of Atrazhev-Timoshkin[2], and represent the worlds best measurement in the region between 350 to 2000 V/cm. The quantum efficiency of the gold photocathode, the drift velocity and longitudinal diffusion coefficients in gas argon are also presented.