One atom in an optical cavity: Spatial resolution beyond the standard diffraction limit

The position of a slow atom passing through a standing-wave light field in an ultrahigh-finesse optical resonator can be measured by observing either the intensity of the light transmitted through the cavity or its phase. Apart from the periodicity of the standing wave, both techniques allow to determine the position of the particle with a resolution much better than the standard classical diffraction limit /2. Position measurements with uncertainty </20 seem to be possible with all-optical techniques.These notes were prepared to celebrate H. Walther's 60th birthday and to honour his pioneering contributions to some of the most lively fields of quantum optics