  Detection of the weakest forces in nature and the search for new physics are
aided by increasingly sensitive measurements of the motion of mechanical
oscillators. However, the attainable knowledge of an oscillator's motion is
limited by quantum fluctuations that exist even if the oscillator is in its
lowest possible energy state. Here we demonstrate a widely applicable technique
for amplifying coherent displacements of a mechanical oscillator with initial
magnitudes well below these zero-point fluctuations. When applying two
orthogonal "squeezing" interactions before and after a small displacement, the
displacement is amplified, ideally with no added quantum noise. We implement
this protocol with a trapped-ion mechanical oscillator and measure an increase
of up to 17.5(3) decibels in sensitivity to small displacements.
