Reading noise squeezing from one antiresonance

Determining how far a driven nonlinear resonator has squeezed its own ther-mal motion means recording a series of sideband spectra while a probe tone is stepped across the band. EP 4 389 308 B1 covers a probe design that yields the same reading from one acquisition.

• Precision measurement technology
• Development of nanomechanical and microelectromechanical resonators
• Manufacture of membrane resonators
• University physics groups that characterize driven resonators

Offer: Research and development collaboration. After that: time-limited evalua-tion; contract research; license.

A driven nonlinear mechanical resonator redistributes its own thermal noise be-tween the quadratures, two conjugate components of its motion—squeezed in one, stretched in the other. The resonator is already running; an instrument reads what comes out of it. A probe tone added to the drive produces sidebands one probe frequency away from the drive line, the line at the drive frequency fd. 

When the tone is stepped across the band, the superimposed spectra show a dip on the low-frequency side of that line: the antiresonance. The position of this antiresonance is the measured quantity. That the frequency of a single antireso-nance measures how far the noise is squeezed is published physics.

The closer the antiresonance lies to the drive line, the stronger the squeezing; that holds only on the upper branch of the Duffing response, the branch with the larger amplitude. The antiresonance never lies closer to the drive line than the linewidth, Γ/2π = 13.5 Hz for the published device. The published derivation is first order in the probe amplitude, so the probe signal must stay weak enough for the derivation to hold.

Reading the antiresonance frequency was itself published—in 2021, with the in-ventors among the authors—and claim 1 concedes that reading to the prior art in its preamble. What claim 1 adds is the design of the probe signal.

The published route steps a single probe tone across the band, one acquisition per frequency—in the published measurement of the antiresonance, roughly a hundred successive acquisitions for one reading. The claimed probe signal carries many tones at once. According to the patent description, it is meant to make the antiresonance readable as a single dip from a single acquisition. Dependent claim 4 additionally specifies that this probe signal stays unchanged during the reading—the stepped probe tone, by contrast, is changed step by step.

What was measured

The patent has been granted; the experimental proof of concept concerns the reading from the antiresonance. Measured, with a single probe tone stepped across the band, on a single silicon nitride membrane resonator, and published in 2021 after peer review:

• membrane of about 0.5 × 0.5 mm², roughly 500 nm thick, in vacuum at 10⁻⁶ mbar and room temperature;
• fundamental mode of the flexural vibration at f₀ ≈ 250.85 kHz, linewidth Γ/2π = 13.5 Hz;
• drive at fd = 251 kHz (among other conditions), probe tone below 1 kHz, sideband spectrum as power versus offset from the drive line;
• antiresonance frequency determined under several drive conditions, each with error bars of ±10 Hz.

Yang F., Fu M., Bosnjak B., Blick R. H., Jiang Y., Scheer E., Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators, Phys. Rev. Lett. 127, 184301 (2021), doi:10.1103/PhysRevLett.127.184301. Open access as arXiv:2107.10355.

EP 4 389 308 B1, granted February 4, 2026. In force as a European patent with unitary effect in the 18 participating member states, and as national parts in Switzerland/Liechtenstein and the United Kingdom. Twenty-one jurisdictions are recorded as in force. The patent family has no member outside Europe. A Ger-man national application runs in parallel. Owner: University of Konstanz.