Long-Lived Coherence between Incoherent Excitons revealed by Time-Resolved ARPES: An Exact Solution

We investigate the exciton dynamics in an exactly solvable two-band model for semiconductors. The model incorporates light-matter, electron-electron and electron-phonon interactions, and captures exciton formation as well as the transition from the coherent to the incoherent regime. We analyze excitonic polarization, populations and coherences, with special focus on their impact in Time-Resolved and Angle-Resolved Photoemission Spectroscopy (TR-ARPES). For nonresonant pumping with below-gap photon energies, TR-ARPES spectra reveal distinct excitonic replica and quantum beats persisting in the incoherent regime. These are due to a coherence between different species of {\em incoherent} excitons. Such type of coherence is resistant to phonon dephasing, indicating that it follows different dynamics than those governing the coherences considered so far.