Figure 1: Scheme for measuring the change of the length of an optical cavity.

N atoms (or ions) are trapped at fixed positions in two two-dimensional optical lattices perpendicular to the cavity axis. A dipole transition of the atoms is in resonance with a single, leaky cavity mode. The atoms are initially prepared in a dark state in which destructive interference prevents the photons from being transferred from the atoms to the cavity mode. When the cavity length L changes by a small amount δL, the true dark states evolve, and the initial state is exposed to collective decoherence, detectable by photons leaking out through the semi-reflecting mirror at a rate proportional to N². This allows to measure δL/L with a Heisenberg-limited uncertainty of order 1/N, even if the initial dark state is a product state.