  Quantum sensing and quantum information processing use quantum advantages
such as squeezed states that encode a quantity of interest with higher
precision and generate quantum correlations to outperform classical methods. In
harmonic oscillators, the rate of generating squeezing is set by a quantum
speed limit. Therefore, the degree to which a quantum advantage can be used in
practice is limited by the time needed to create the state relative to the rate
of unavoidable decoherence. Alternatively, a sudden change of harmonic
oscillator's frequency projects a ground state into a squeezed state which can
circumvent the time constraint. Here, we create squeezed states of atomic
motion by sudden changes of the harmonic oscillation frequency of atoms in an
optical lattice. Building on this protocol, we demonstrate rapid quantum
amplification of a displacement operator that could be used for detecting
motion. Our results can speed up quantum gates and enable quantum sensing and
quantum information processing in noisy environments.
