  Measurement-based cooling is a method by which a quantum system, initially in
a thermal state, can be prepared 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
pre-cooled by Doppler laser cooling to a thermal state with a mean excitation
of $\bar n \approx 18$ 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 can be
applied to other systems that are not as amenable to laser cooling as trapped
ions.
