Photon–Phonon Atomic Coherence Interaction of Nonlinear Signals in Various Phase Transitions Eu³⁺: BiPO₄

We report photon–phonon atomic coherence (cascade- and nested-dressing) interaction from the various phase transitions of Eu³⁺: BiPO₄ crystal. Such atomic coherence spectral interaction evolves from out-of-phase fluorescence to in-phase spontaneous four-wave mixing (SFWM) by changing the time gate. The dressing dip switch and three dressing dips of SFWM result from the strong photon–phonon destructive cross- and self-interaction for the hexagonal phase, respectively. More phonon dressing results in the destructive interaction, while less phonon dressing results in the constructive interaction of the atomic coherences. The experimental measurements of the photon–phonon interaction agree with the theoretical simulations. Based on our results, we proposed a model for an optical transistor (as an amplifier and switch).