Electron dynamics induced by quantum cat-state light

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 electron density matrix evolves as an average over trajectories $\{{\rho }_{\alpha }\}$ weighted by the Sudarshan–Glauber $P$ distribution $P(\alpha )$ in the weak light–matter coupling regime. Each trajectory obeys an equation of motion, $\mathrm{i}{\mathrm{\partial }}_t{\rho }_{\alpha }={\mathcal{H}}_{\alpha }{\rho }_{\alpha }-{\rho }_{\alpha }{\mathcal{H}}_{\alpha }$, 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 $\mathrm{i}{\mathrm{\partial }}_t\rho =\mathcal{H}\rho -\rho {\mathcal{H}}^{†}$, 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.