  We show experimentally that a broad class of interactions involving quantum
harmonic oscillators can be made stronger (amplified) using a unitary squeezing
protocol. While our demonstration uses the motional and spin states of a single
trapped $^{25}$Mg$^{+}$ ion, the scheme applies generally to Hamiltonians
involving just a single harmonic oscillator as well as Hamiltonians coupling
the oscillator to another quantum degree of freedom such as a qubit, covering a
large range of systems of interest in quantum information and metrology
applications. Importantly, the protocol does not require knowledge of the
parameters of the Hamiltonian to be amplified, nor does it require a
well-defined phase relationship between the squeezing interaction and the rest
of the system dynamics, making it potentially useful in instances where certain
aspects of a signal or interaction may be unknown or uncontrolled.
