Electron-phonon coupling is a major decoherence mechanism, which often causes scattering and energy dissipation in semiconductor electronic systems. However, this electron-phonon coupling may be used in a positive way for reaching the strong or ultra-strong coupling regime in an acoustic version of the cavity quantum electrodynamic system. Here we propose and demonstrate a phonon cavity for surface acoustic waves, which is made of periodic metal fingers that constitute Bragg reflectors on a GaAs/AlGaAs heterostructure. Phonon band gap and cavity phonon modes are identified by frequency, time and spatially resolved measurements of the piezoelectric potential. Tunneling spectroscopy on a double quantum dot indicates the enhancement of phonon assisted transitions in a charge qubit. This encourages studying of acoustic cavity quantum electrodynamics with surface phonons.
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