  Triply resonant three mode interactions in long optical cavities have been
shown to lead to enhanced scattering of carrier light by the ultrasonic
acoustic modes of the test mass mirrors. At high optical power, this can lead
to parametric instability (parametric gain R > 1) for a few acoustic modes with
strong spectral and spatial overlap. Numerous ?~10^3 acoustic modes of the test
masses are predicted to have R > 10^2. Experimental studies have shown that
such modes also strongly scatter the carrier light, enabling very sensitive
readout of the acoustic modes. The 3-mode scattering from the thermal
fluctuation of large population of ultrasonic modes would causes random changes
in occupation number of the carrier light and cavity transverse optical modes.
Because the thermal fluctuation time scale (set by the acoustic mode relaxation
times) is typically a few seconds, the noise spectrum from thermally induced
photon number fluctuations is strongly peaked at low frequency. The noise level
depends on the acoustic mode structure and acoustic losses of the test masses,
the transverse optical mode spectrum of the optical cavities and on the test
mass temperature. We theoretically investigate the possible effect of this
noise and show that in advanced detectors under construction three mode
interaction noise is below the standard quantum limit, but could set limits on
future low frequency detectors that aim to exceed the free mass standard
quantum limit.
