We show that projective measurements on quantum light can induce macroscopic cat states in many-electron systems driven by such light. Here we investigate the quantum dynamics of $N$ independent two-level electrons interacting with Schrödinger-cat or -kitten states of light. Without measurement, a macroscopic cat state of the electrons appears only in an ultrashort time window. In contrast, we demonstrate that photon-number parity or quadrature projective measurements can restore a macroscopic cat state in nonequilibrium electrons, even in the thermodynamic limit. These dynamics are captured by an external-field approximation, in which the electronic system evolves into a Rabi-oscillation cat state. Our results highlight the need for precise quantum measurement techniques for light to control macroscopic quantum states of matter driven by quantum light.

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• Light-matter interaction
• Quantum macroscopicity
• Quantum measurements
• Ultrafast phenomena
• Two-level models