Collective dynamics of multimode bosonic systems induced by weak quantum measurement

In contrast to strong projective measurement, which freezes the system evolution by quantum Zeno effect, weak measurement can effectively compete with standard unitary dynamics leading to nontrivial effects. Here we consider global weak measurement addressing several bosonic modes at the same time, 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. 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 for constant external measurement, 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