  We provide a number-conserving approach to the backreaction problem of small
quantum fluctuations onto a classical background for the exactly soluble
dynamical evolution of a Bose-Einstein condensate, experimentally realizable in
the ultracold gas laboratory. A force density exerted on the gas particles
which is of quantum origin is uniquely identified as the deviation from the
classical Eulerian force density. The backreaction equations are then explored
for the specific example of a finite size uniform density condensate initially
at rest. By assuming that the condensate starts from a non-interacting regime,
and in its ground state, we fix a well-defined initial vacuum condition, which
is driven out-of-equilibrium by instantaneously turning on the interactions.
The assumption of this initial vacuum accounts for the ambiguity in choosing a
vacuum state for interacting condensates, which is due to phase diffusion and
the ensuing condensate collapse. As a major finding, we reveal that the time
evolution of the condensate cloud leads to condensate density corrections that
cannot in general be disentangled from the quantum depletion in measurements
probing the power spectrum of the total density. Furthermore, while the
condensate is initially at rest, quantum fluctuations give rise to a nontrivial
condensate flux, from which we demonstrate that the quantum force density
attenuates the classical Eulerian force. Finally, the knowledge of the particle
density as a function of time for a condensate at rest determines, to order
$N^0$, where $N$ is the total number of particles, the quantum force density,
thus offering a viable route for obtaining experimentally accessible quantum
backreaction effects.
