  Coupled nanomechanical resonators have recently attracted much attention for
both fundamental studies in physics and broad applications in high-precession
detection or sensing. By studying the Landau-Zener transitions and Rabi
oscillation of two coupled resonators, it has been shown that such a two-mode
system acts as a classical two-level system bearing the analog to a quantum
mechanical two-level one. Here we construct a St\"uckelberg interferometer with
two coupled cantilevers by driving the system through the avoided crossing
twice. By measuring the non-adiabatic phase acquired at the Landau-Zener
transition, we unveil an in-depth analog between the two-mode and quantum
two-level systems. Our study opens up new opportunities for constructing
interferometers with classical devices.
