Optical kaleidoscope using a single atom

A new method to track the motion of a single particle in the field of a high-finesse optical resonator is analyzed. It exploits sets of near-degenerate higher-order Gaussian cavity modes, whose symmetry is broken by the position dependent phase shifts induced by the particle. Observation of the spatial intensity distribution outside the cavity allows direct determination of the particle's position. This is demonstrated by numerically generating a realistic atomic trajectory using a semiclassical simulation and comparing it to the reconstructed path. The path reconstruction itself requires no knowledge about the forces on the particle. Experimental realization strategies are discussed