  Quantum acoustic systems, which integrate surface or bulk phonons with
superconducting qubits, offer a unique opportunity to investigate phononic
$interference$ and $scattering$ processes in the quantum regime. In particular
the interaction between a superconducting qubit and a phononic oscillator
allows the qubit to sense the oscillator's excitation spectrum and underlying
interference effects. Here we present measurements revealing Fano interference
of a resonantly trapped piezoelectric surface acoustic wave (SAW) mode with a
broad continuum of surface phonons in a system consisting of a SAW resonator
coupled to a superconducting qubit. The experiments highlight the existence of
additional weakly coupled mechanical modes and their influence on the
qubit-phonon interaction and underscore the importance of phononic interference
in quantum acoustic architectures that have been proposed for quantum
information processing applications.
