  We extend our theory of Bloch oscillations of cold atoms inside an optical
cavity [ Venkatesh et al. Phys. Rev. A 80 063834 (2009)] to include the effects
of quantum noise arising from coupling to external modes. The noise acts as a
form of quantum measurement backaction by perturbing the coupled dynamics of
the atoms and the light. We take it into account by solving the
Heisenberg-Langevin equations for linearized fluctuations about the atomic and
optical mean fields and examine how this influences the signal-to-noise ratio
of a measurement of external forces using this system. In particular, we
investigate the effects of changing the number of atoms, the intracavity
lattice depth, and the atom-light coupling strength, and show how resonances
between the Bloch oscillation dynamics and the quasiparticle spectrum have a
strong influence on the signal-to-noise ratio, as well as heating effects. One
of the hurdles we overcome in this paper is the proper treatment of
fluctuations about time-dependent mean fields in the context of cold-atom
cavity QED.
