  Quantum confinement leads to the formation of discrete electronic states in
quantum dots. Here we probe electron-phonon interactions in a suspended InAs
nanowire double quantum dot (DQD) that is electric-dipole coupled to a
microwave cavity. We apply a finite bias across the wire to drive a steady
state population in the DQD excited state, enabling a direct measurement of the
electron-phonon coupling strength at the DQD transition energy. The amplitude
and phase response of the cavity field exhibit features that are periodic in
the DQD energy level detuning due to the phonon modes of the nanowire. The
observed cavity phase shift is consistent with theory that predicts a
renormalization of the cavity center frequency by coupling to phonons.
