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.
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