Limits to the sensitivity of a low noise compact atomic gravimeter

30 pages, 14 figuresInternational audienceA detailed analysis of the most relevant sources of phase noise in an atomic interferometer is carried out, both theoretically and experimentally. Even a short interrogation time of 100 ms allows our cold atom gravimeter to reach an excellent short term sensitivity to acceleration of $1.4\times 10^{-8}$g at 1s. This result relies on the combination of a low phase noise laser system, efficient detection scheme and good shielding from vibrations. In particular, we describe a simple and robust technique of vibration compensation, which is based on correcting the interferometer signal by using the AC acceleration signal measured by a low noise seismometer