Inducing macroscopic cat states of nonequilibrium electrons via cat-state light irradiation and projective measurements

We show that projective measurements on quantum light can induce macroscopic cat states in many-electron systems driven by large-amplitude cat-state 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 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.