  We develop a system for measurements of power spectra of transmitted light
intensity fluctuations, in which the extraneous noise, including shot noise, is
reduced. In essence, we just apply light, measure the power of the transmitted
light and derive its power spectrum. We use this to observe the spontaneous
noise spectra of photon atom interactions. Applying light with frequency
modulation, we can also observe the spontaneous noise reflecting the coherence
between the hyperfine levels in the excited state. There are two in novel
components in the measurement system, the noise reduction scheme and the
stabilization of the laser system. The noise reduction mechanism can be used to
reduce the shot noise contribution to arbitrarily low levels through averaging,
in principle. This is combined with differential detection to keep unwanted
noise at low levels. The laser system is stabilized to obtain spectral width
below 1\,kHz without high frequency ($\gtrsim10\,$MHz) noise. These methods are
described systematically and the performance of the asurement system is
examined through experimental results.
