Fig. 3: Phase jump extraction in the transition regime.

a Phase \(\theta\) of the 1D FFT extracted along linecuts parallel to the phase jumps in (b). The phase is evaluated at the dominant frequency in the FFT amplitude spectrum for the linecuts in between phase jumps. A linear increase in phase extracted from regions without phase jumps is subtracted off to make the phase jump magnitude evident as the vertical shift between plateaus in panel (a). From this data we extract an average \(\Delta \theta /2\pi \, \approx \, -0.47,\) reflecting approximately half of an electron repelled from the outer EC for each charge added to the inner EC within this range of \({V}_{{{\rm{MG}}}}\). Inset: illustration of the coupling \({K}_{12}\) between the outer and inner ECs contributing to the phase jumps. b Conductance \({G}_{{{\rm{D}}}}\) oscillations on the outer EC with \({V}_{{{\rm{PG}}}}\) and \({V}_{{{\rm{MG}}}}\) near the center of the transition regime showing periodic phase jumps along the dashed black lines. Note that increasing \({V}_{{{\rm{MG}}}}\) adds electrons to the system or equivalently increases phase, so the phase jumps correspond to negative shifts in phase i.e., repulsion of electrons from the FP cavity. Similar interference patterns are observed in both the strong and weak QPC backscattering regimes (Supplementary Fig. 4) as well as at elevated temperatures (Supplementary Fig. 5).