Exchange-controlled quantum beats and entanglement in an exciton--bimodal-cavity system
We theoretically demonstrate tunable population transfer and entanglement generation in a two-exciton system coupled to a bimodal optical cavity, including an exciton-exciton exchange interaction. By using dressed-state transformations and Löwdin partitioning, we derive effective Hamiltonians that identify three dynamical time scales: local polaritonic oscillations, long-period dressed-state beats, and direct excitonic exchange. We apply the framework to graphene nanoribbon excitons, using excitonic energies, transition dipoles, and lifetimes obtained from first-principles calculations to parameterize the model. In the small- and moderate-exchange regimes, the dynamics become multiscale, and the beat channel sustains sizable quantum entanglement over long dissipative time windows. In the large-exchange regime, the excitonic Hamiltonian dominates and drives nearly complete population transfer between excitonic states over many coherent cycles. The resulting analytical expressions provide direct design rules connecting the beat period, transfer amplitude, and coherent-cycle number to the exchange interaction, cavity detuning, and light--matter coupling. Our results establish a controllable route for engineering long-lived entanglement and coherent excitonic operations in exciton--bimodal-cavity systems.