Measurement-based cooling is a method by which a quantum system, initially in a thermal state, can be
prepared probabilistically in its ground state through some sort of measurement. This is done by making a
measurement that heralds the system being in the desired state. Here we demonstrate the application of a
measurement-based cooling technique to a trapped atomic ion. The ion is precooled by Doppler laser cooling
to a thermal state with a mean excitation of ¯n ≈ 18 and the measurement-based cooling technique selects those
occasions when the ion happens to be in the motional ground state. The fidelity of the heralding process is greater
than 95%. This technique could be applied to other systems that are not as amenable to laser cooling as trapped
ions.