  In contrast to the fully projective limit of strong quantum measurement,
where the evolution is locked to a small subspace (quantum Zeno dynamics), or
even frozen completely (quantum Zeno effect), the weak non-projective
measurement can effectively compete with standard unitary dynamics leading to
nontrivial effects. Here we consider global weak measurement addressing
collective variables, thus preserving quantum superpositions due to the lack of
which path information. While for certainty we focus on ultracold atoms, the
idea can be generalized to other multimode quantum systems, including various
quantum emitters, optomechanical arrays, and purely photonic systems with
multiple-path interferometers (photonic circuits). We show that light
scattering from ultracold bosons in optical lattices can be used for defining
macroscopically occupied spatial modes that exhibit long-range coherent
dynamics. Even if the measurement strength remains constant, the quantum
measurement backaction acts on the atomic ensemble quasi-periodically and
induces collective oscillatory dynamics of all the atoms. We introduce an
effective model for the evolution of the spatial modes and present an analytic
solution showing that the quantum jumps drive the system away from its stable
point. We confirm our finding describing the atomic observables in terms of
stochastic differential equations.
