  The Michelson interferometer is a cornerstone of experimental physics. Its
applications range from providing first impressions of wave interference in
educational settings to probing spacetime at minuscule precision scales.
Interferometer precision provides a unique view of the fundamental medium of
matter and energy, enabling tests for new physics as well as searches for the
gravitational wave signatures of distant astrophysical events. Optical
interferometers are typically operated by continuously measuring the power at
their output port. Signal perturbations then create sideband fields, forming a
beat-note with the fringe light that modulates that power. When operated at a
nearly-dark destructive interference fringe, this readout is a form of homodyne
detection, with an imprecision set by a ``standard quantum limit'' attributed
to shot noise from quantum vacuum fluctuations. The sideband signal fields
carry energy which can, alternatively, be directly observed as photons distinct
from the source laser. Without signal energy, vacuum does not form sidebands
and cannot spuriously create photon counts or shot noise. Thus, counting can
offer improved statistics when searching for weak signals when classical
backgrounds are below the standard quantum limit. Here, photon counting
statistics are described for optical interferometry, relating the two forms of
measurement and showing cases where counting greatly outperforms homodyne
readout, even with squeezed state quantum enhancement. The most immediate
application for photon counting is improving searches of stochastic signals,
such as from quantum gravity or from new particle fields. The advantages of
counting may extend to wider applications, such as gravitational wave
detectors, and the concept of Fisher-information representative spectral
density is introduced to motivate further study.
