Electron dynamics induced by quantum cat-state light

Abstract

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 $\{\ddot{I}{}_{\hat{I}}\pm \}$ weighted by the Sudarshan--Glauber $P$ distribution $P(\hat{I}\pm )$ in the weak light--matter coupling regime. Each trajectory obeys an equation of motion, $\mathrm{i}{\partial }_t\ddot{I}{}_{\hat{I}}\pm ={\mathcal{H}}_{\hat{I}}\pm \ddot{I}{}_{\hat{I}}\pm -\ddot{I}{}_{\hat{I}}\pm {\mathcal{H}}_{\hat{I}}\pm$, where an effective Hamiltonian ${\mathcal{H}}_{\hat{I}}\pm$ 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 $\ddot{I}{}_{\hat{I}}\pm$. This non-Hermitian dynamics differs from the conventional one observed in open quantum systems, described by $\mathrm{i}{\partial }_t\ddot{I}=\mathcal{H}\ddot{I}-\ddot{I}{\mathcal{H}}^{†}$, 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.

10 pages, 2 figures (including supplemental material)