The pursuit of room temperature quantum optomechanics with tethered
nanomechanical resonators faces stringent challenges owing to extraneous
mechanical degrees of freedom. An important example is thermal intermodulation
noise (TIN), a form of excess optical noise produced by mixing of thermal noise
peaks. While TIN can be decoupled from the phase of the optical field, it
remains indirectly coupled via radiation pressure, implying a hidden source of
backaction that might overwhelm shot noise. Here we report observation of TIN
backaction in a high-cooperativity, room temperature cavity optomechanical
system consisting of an acoustic-frequency Si3βN4β trampoline coupled to a
Fabry-P\'{e}rot cavity. The backaction we observe exceeds thermal noise by 20
dB and radiation pressure shot noise by 40 dB, despite the thermal motion being
10 times smaller than the cavity linewidth. Our results suggest that mitigating
TIN may be critical to reaching the quantum regime from room temperature in a
variety of contemporary optomechanical systems.Comment: 8 pages, 5 figure