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A many-body atomic system coupled to quantized light is subject to weakmeasurement. Instead of coupling light to the on-site density, we consider thequantum backaction due to the measurement of matter-phase-related variablessuch as global phase coherence. We show how this unconventional approach opensup new opportunities to affect system evolution and demonstrate how this canlead to a new class of measurement projections, thus extending the measurementpostulate for the case of strong competition with the system's own evolution.

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