Optomechanical thermal intermodulation noise

Thermal fluctuations limit the sensitivity of precision measurements ranging from laser interferometer gravitational wave observatories to optical atomic clocks. In optical cavities, thermally induced fluctuations of length or refractive index create frequency noise. Here we investigate a previously unreported broadband noise process, thermal intermodulation noise, originating from the transduction of frequency fluctuations by the inherent nonlinearity of the cavity-laser detuning response. We show that the Brownian motion of a thin Si$_3$N$_4$ membrane in an optomechanical cavity at room temperature, instead of transducing into the phase quadrature only, also creates intensity noise for resonant laser excitation. We study the laser detuning dependence of this noise and also demonstrate that its magnitude scales with the quartic power of the ratio of the optomechanical coupling rate to the cavity linewidth. Both dependencies are in excellent agreement with our developed theoretical model. We use a phononic crystal membrane with a low mass, soft-clamped defect mode and operate in a regime where quantum fluctuations of radiation pressure are expected to dominate the motion of the membrane (i.e. a nominal quantum cooperativity of unity). However, we find that the thermal intermodulation noise exceeds the vacuum fluctuations by more than two orders of magnitude, even within the phononic bandgap, thereby preventing the observation of ponderomotive squeezing. Our work shows that a new noise source arises as a consequence of nonlinear cavity transduction, which is broadly relevant to cavity-based measurements, and is especially pronounced when thermally induced frequency fluctuations are comparable to the optical linewidth.