  We revisit the problem of preparing a mechanical oscillator in the vicinity
of its quantum-mechanical ground state by means of feedback cooling based on
continuous optical detection of the oscillator position. In the parameter
regime relevant to ground state cooling, the optical back-action and
imprecision noise set the bottleneck of achievable cooling and must be
carefully balanced. This can be achieved by adapting the phase of the local
oscillator in the homodyne detection realizing a so-called variational
measurement. The trade-off between accurate position measurement and minimal
disturbance can be understood in terms of Heisenberg's microscope and becomes
particularly relevant when the measurement and feedback processes happen to be
fast within the quantum coherence time of the system to be cooled. This
corresponds to the regime of large quantum cooperativity
$C_{\text{q}}\gtrsim1$, which was achieved in recent experiments on feedback
cooling. Our method provides a simple path to further pushing the limits of
current state-of-the-art experiments in quantum optomechanics.

Quantum Physics;Mesoscale and Nanoscale Physics