A behavior typical of amorphous solids has been observed at very low temperatures for a layer obtained by ion implanting a quartz substrate. A surface‐acoustic‐wave velocity variation has been measured between 0.9 and 6 K for crystalline and implanted quartz by building a 960‐MHz delay line oscillator. The quartz substrate was implanted with helium ions at 95 keV. Over a limited temperature range, the velocity on the implanted surface is proportional to the logarithm of the temperature according to the off‐diagonal interaction between the acoustic wave and a broad distribution of two level defects. An increase of the proportionality coefficient is produced by an annealing at 567 °C and it seems related to a decrease of the specific mass. Moreover, the defect density of states is smaller than that of vitreous silica.