Electron dynamics induced by quantum cat-state light

TL;DR

This paper develops an effective theory describing electron dynamics driven by quantum cat-state light, revealing non-Hermitian behavior due to quantum interference, with results confirmed by simulations of the electron-photon system.

Contribution

The paper introduces a novel effective theory for electron dynamics under quantum cat-state light, highlighting non-Hermitian effects from quantum interference.

Findings

Electron density matrix evolves as an average over trajectories with a non-Hermitian Hamiltonian.

The theory agrees with full system simulations for the Dicke model.

Quantum interference transfers optical effects to electrons, producing exotic dynamics.

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 $\{\rho_\alpha\}$ weighted by the Sudarshan--Glauber $P$ distribution $P(\alpha)$ in the weak light--matter coupling regime. Each trajectory obeys an equation of motion, $\mathrm{i} \partial_t\rho_\alpha=\mathcal{H}_{\alpha} \rho_\alpha-\rho_\alpha\mathcal{H}_{\alpha}$, 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 $\mathrm{i} \partial_t\rho=\mathcal{H}\rho-\rho \mathcal{H}^\dagger$, 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.