We present an effective theory for describing electron dynamics driven by an optical external field in a Schrödinger's cat state. We show that the reduced electron density matrix evolves as an average over trajectories $\left\{{\rho }_{\alpha }\right\}$ weighted by the Sudarshan-Glauber $P$ distribution $P\left(\alpha \right)$ in the weak light-matter coupling regime. Each trajectory obeys an equation of motion, $\mathrm{i}{\partial }_t{\rho }_{\alpha }={\mathcal{H}}_{\alpha }{\rho }_{\alpha }-{\rho }_{\alpha }{\mathcal{H}}_{\alpha }$, where an effective Hamiltonian ${\mathcal{H}}_{\alpha }$ 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 ${\rho }_{\alpha }$. This non-Hermitian dynamics differs from the conventional one observed in open quantum systems, described by $\mathrm{i}{\partial }_t\rho =\mathcal{H}\rho -\rho {\mathcal{H}}^{†}$, which has complex conjugation in the second term. We confirm that the reduced, trajectory-resolved effective theory agrees with full electron-photon simulations for the few-electron Dicke model, thereby validating the interferential non-Hermitian description in the weak-coupling regime.

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• Quantum description of light-matter interaction
• Quantum interference effects
• Non-Hermitian systems