Quantum State Reduction by Matter-Phase-Related Measurements in Optical Lattices

A many-body atomic system coupled to quantized light is subject to weak measurement. Instead of coupling light to the on-site density, we consider the quantum backaction due to the measurement of matter-phase-related variables such as global phase coherence. We show how this unconventional approach opens up new opportunities to affect system evolution and demonstrate how this can lead to a new class of measurement projections, thus extending the measurement postulate for the case of strong competition with the system's own evolution.