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).

We report atomic-like Autler–Townes splitting controlled by destructive and constructive natural non-Hermitian quantization in Eu3+: BiPO4. For the first time, we explored destructive and constructive AT splitting in different regions. Fluorescence (FL), spontaneous four-wave mixing (SFWM), and shot noise signals exhibit different kinds of AT splitting. FL signal exhibits three level dip AT splitting through destructive quantization, SFWM signals exhibit peak and multi-dip AT splitting through constructive quantization, and shot noise signals exhibit a two-level dip AT splitting. These kinds of AT splitting originate through single photon dressing and double photon–phonon dressing, which can be controlled by adjusting experimental parameters. Our atomic-like Autler–Townes-splitting technique is useful for making a spectral router.

We demonstrated photon destructive quantization and optical bistability in Eu³⁺:NaYF₄ and Sm³⁺:BiPO₄. Photon destructive quantization transitions FL dip to a sharp peak of SFWM via external field, with bistability controlled by TGP and TGW.

In this paper, we explore the asymmetry observed between the effects of photon–phonon coupling (nested-dressing) and a crystal field (CF) on the fine structure of fluorescence (FL) and spontaneous four-wave mixing (SFWM) in Eu³⁺: BiPO₄ and Eu³⁺: NaYF₄. The competition between the CF and the strong photon–phonon dressing leads to dynamic splitting in two directions. The CF leads to static splitting in one direction under weak phonon dressing. The evolution from strong dressing to weak dressing results in spectral asymmetry. This spectral asymmetry includes out-of-phase FL and in-phase SFWM. Further, the large ratio between the dressing Rabi frequency and the de-phase rate leads to strong FL and SFWM asymmetry due to photon–phonon constructive dressing. Moreover, the experimental results suggest the analogy of a spectra asymmetry router with a channel equalization ratio of 96.6%.

We report super broad non-Hermitian line shape from out-of-phase and in-phase photon-phonon dressing (quantization) in Eu³⁺: NaYF₄ and Eu³⁺: BiPO₄ nanocrystals. The line shape is controlled by changing time gate position, time gate width, power, temperature, sample, photomultiplier tubes, and laser. We observed that the fluorescence (FL) line-shape contrasts are 69.23% for Eu³⁺: BiPO₄ and 43.75% for Eu³⁺: NaYF₄, owing to the stronger out-of-phase photon-phonon dressing (destructive quantization). Moreover, we observed that the spontaneous four-wave mixing (SFWM) line shape was approximately three times wider at 300 K than at 77 K for the [(12:1)-phase] Eu³⁺: NaYF₄ due to more high-frequency in-phase phonon dressing (strong constructive quantization). Furthermore, we showed that the noise line-shape width remains unchanged for Eu³⁺: BiPO₄ (16 nm) and Eu³⁺: NaYF₄ (12 nm) due to out-of-phase and in-phase photon-phonon dressing balance. Such results have potential applications in multi-channel band stop filter.