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Coupled nanomechanical resonators have recently attracted much attention forboth fundamental studies in physics and broad applications in high-precessiondetection or sensing. By studying the Landau-Zener transitions and Rabioscillation of two coupled resonators, it has been shown that such a two-modesystem acts as a classical two-level system bearing the analog to a quantummechanical two-level one. Here we construct a St\"uckelberg interferometer withtwo coupled cantilevers by driving the system through the avoided crossingtwice. By measuring the non-adiabatic phase acquired at the Landau-Zenertransition, we unveil an in-depth analog between the two-mode and quantumtwo-level systems. Our study opens up new opportunities for constructinginterferometers with classical devices.

Classical analog of St\"uckelberg interferometry with two coupled mechanical resonators