Minimally-destructive detection of magnetically-trapped atoms using frequency-synthesised light

We present a technique for atomic density measurements by the off-resonant phase-shift induced on a two-frequency, coherently-synthesised light beam. We have used this scheme to measure the column density of a magnetically trapped atom cloud and to monitor oscillations of the cloud in real time by making over a hundred non-destructive local density measurments. For measurements using pulses of 10,000-100,000 photons lasting ~10 microsecond, the precision is limited by statistics of the photons and the photodiode avalanche. We explore the relationship between measurement precision and the unwanted loss of atoms from the trap and introduce a figure of merit that characterises it. This method can be used to probe the density of a BEC with minimal disturbance of its phase.