Fig. 4: Phonon interferomeric probe.

Dispersive state-dependent interferometric probe. a Schematic roles played by each element. b Blue (salmon) points show the φ dependence of Q₁’s final P_e when Q₂ is in \(\left|g\right\rangle\) (\(\left|e\right\rangle\)), showing a dependence of the phonon phase on Q₂’s state, with a shift of ~0.4π rad. c Qubit pulse sequences (see text for details). d Schematic roles played by each element for the dispersive phase-dependent interferometric probe. e Ramsey interference in Q₂ (blue circles) reveals Q₂’s dependence on the relative phase with the phonon. When repeating the same protocol with no initial π pulse on Q₁, we measure the Ramsey interference of Q₂ (salmon squares), shifted by π compared to the first measurement. Blue (salmon) points show the φ dependence of Q₁’s final P_e when Q₂ is in \(\left|g\right\rangle\) (\(\left|e\right\rangle\)), showing a dependence of the phonon phase on Q₂’s state, with a shift of ~0.4π rad. f Qubit pulse sequences, similar to c except Q₂ is always placed in \((\left|g\right\rangle +{e}^{{{{{{\rm{i}}}}}}\theta }\left|e\right\rangle )/\sqrt{2}\) and the θ-dependent \({P}_{e}^{Q2}\) is measured.