Fig. 3: Characterization of two-mode mechanical spectra and their sensitivity in thermal motion by balanced homodyne interferometry.

a Two-mode power spectral density of thermal motion observed by balanced homodyne interferometry with an optical probe power of 3 μW. The insets show the fundamental flexural mode calculated by the finite element method (the color code corresponds to the amount of displacement, and the black vectors depict the vibration directions). b Two-mode power spectral density of thermal motion with different optical probe powers. The lowest noise floor level, —\({S}_{{\rm{floor}}}=8.2\times 1{0}^{-13}\,{\rm{m}}/\sqrt{{\rm{Hz}}}\)—, was achieved with the optical probe power of 15 μW. c Two-mode power spectral density of thermal motion with respect to y coordinate. d Normalized difference between integral of power spectral density for modes η(y) with respect to y coordinate. The black dots show the experimental data and the red solid curve shows the fitted curve with θ₀ = 44.9° and an tilted sweep angle ϕ₀ = 1.2°. η has completely different profiles with respect to the initial angle θ₀ between the x-axis and the vibrating direction of a mechanical mode in the nanowire (curves with θ₀ = 0°, 30°, 60°, and 90° are shown with ϕ₀ = 1.2°).