  We demonstrate a new feedback algorithm to cool a single neutral atom trapped
inside a standing-wave optical cavity. The algorithm is based on parametric
modulation of the confining potential at twice the natural oscillation
frequency of the atom, in combination with fast and repetitive atomic position
measurements. The latter serve to continuously adjust the modulation phase to a
value for which parametric excitation of the atomic motion is avoided. Cooling
is limited by the measurement back action which decoheres the atomic motion
after only a few oscillations. Nonetheless, applying this feedback scheme to a
~ 5 kHz oscillation mode increases the average storage time of a single atom in
the cavity by a factor of 60 to more than 2 seconds. In contrast to previous
feedback schemes, our algorithm is also capable of cooling a much faster ~ 500
kHz oscillation mode within just microseconds. This demonstrates that
parametric cooling is a powerful technique that can be applied in all
experiments where optical access is limited.
