Abstract
We present an effective theory for describing electron dynamics driven by an optical external field in a Schr\"{o}dinger's cat state. We show that the electron density matrix evolves as an average over trajectories {ρ_α} weighted by the Sudarshan--Glauber P distribution P(α) in the weak light--matter coupling regime. Each trajectory obeys an equation of motion, i ∂_tρ_α=H_α ρ_α-ρ_αH_α, where an effective Hamiltonian H_α becomes non-Hermitian due to quantum interference of light. The optical quantum interference is transferred to electrons through the asymmetric action between the ket and bra state vectors in ρ_α. This non-Hermitian dynamics differs from the conventional one observed in open quantum systems, described by i ∂_tρ=Hρ-ρ H^†, which has complex conjugation in the second term. We confirm that the results of the effective theory agree with those of full electron--photon system simulations for the few-electron Dicke model, demonstrating experimental accessibility to exotic non-Hermitian dynamics.