Resolving Phonon Number States with an Acoustic Ramsey Interferometer

The rise of quantum control over surface acoustic waves (SAWs) introduced a novel concept: a “giant atom” many wavelengths long. The large size of the atom, formed by a transmon qubit with a piezoelectric transducer, generates fine frequency features in the qubit-phonon interaction strength that are determined by the shape of the transducer. Here, we combine a multi-mode SAW cavity with a qubit whose transducer is spatially engineered to enter the strong dispersive regime. The transducer comprises two halves separated by 38 wavelengths that, in close analogy to Ramsey interferometry, generate narrow frequency fringes in the qubit-phonon coupling. We observe these fringes both as a sharp frequency dependence in the qubit emission of unconfined phonons and as a modulated coupling strength to acoustic cavity modes. This modulation creates frequency regions of strong coupling in close proximity to windows of vanishing coupling, a combination that enables both dispersive operation and a coupling strength that is comparable to the free spectral range. The strong coupling creates a large dispersive shift that exceeds both qubit and acoustic linewidths.