Observation of Quantum Effects in the Spectrum of Piezoelectrically Amplified Acoustic Flux in GaAs

Using x-ray scattering, we have made the first observations of the spectrum of acousto-electrically amplified phonons in the quantum limit, where the conduction-electron system obeys quantum statistics and the observed phonon wave vector $q$ is comparable to the electron Fermi wave vector $k_{\mathrm{F}}$. In GaAs samples with degenerate carrier distributions, we observe a dramatic quantum anomaly consisting of an abrupt decrease in phonon gain for $q$ larger than $2k_{\mathrm{F}}$.