  We apply a large-deviation method to study the diffusive trajectories of the
quadrature operators of light within a reservoir connected to dissipative
quantum systems. We formulate the study of quadrature trajectories in terms of
characteristic operators and show that in the long time limit the statistics of
such trajectories obey a large-deviation principle. We take our motivation from
homodyne detection schemes which allow the statistics of quadrature operator of
the light field to be measured. We illustrate our approach with four examples
of increasing complexity: a driven two-level system, a `blinking' three-level
system, a pair of weakly-coupled two-level driven systems, and the micromaser.
We discuss how quadrature operators can serve as alternative order parameters
for the classification of dynamical phases, which is particularly useful in
cases where the statistics of quantum jumps cannot distinguish between such
phases. The formalism we introduce also allows us to analyse the properties of
the light emitted by quantum jump trajectories which fluctuate far from the
typical dynamics.
