  A fundamental tenet of quantum mechanics is that measurements change a
system's wavefunction to that most consistent with the measurement outcome,
even if no observer is present. Weak measurements produce only limited
information about the system, and as a result only minimally change the
system's state. Here, we theoretically and experimentally characterize quantum
back-action in atomic Bose-Einstein condensates interacting with a far-from
resonant laser beam. We theoretically describe this process using a quantum
trajectories approach where the environment measures the scattered light and
present a measurement model based on an ideal photodetection mechanism. We
experimentally quantify the resulting wavefunction change in terms of the
contrast of a Ramsey interferometer and control parasitic effects associated
with the measurement process. The observed back-action is in good agreement
with our measurement model; this result is a necessary precursor for achieving
true quantum back-action limited measurements of quantum gases.
