We are building an experimental apparatus to investigate quantum non-demolition measurements (QND) and measurement induced squeezing in a cold sample of Rubidium atoms optically confined in a high finesse optical cavity. An atomic beam produced by a 2D MOT is used to load a conventional MOT in a ultra high vacuum chamber. The atoms, after a phase of compression and molasse, are then transfered to a dipole trap, obtained injecting the folded optical cavity on its fundamental mode with radiation at 1560 nm. Lowering the optical potential the sample will be evaporatively cooled till condensation where the two cavity arms cross.
A laser beam at 780 nm resonant with the cavity will provide the tool for the quantum non-demolition measurement inducing spin squeezing. Using multi-frequencies schemes and heterodyne detection techniques it is possible to cancel out several uncertainty sources, as well as measuring both the absolute and the differential population on the two hyperfine levels of the ground state. A high degree of squeezing is expected, as a consequence of the high atomic optical depth determined by the finesse of the optical cavity.