Deterministic relation between thermal-phonon dressings and a non-Hermitian multi-Fano interferences router in ion-doped microcrystals

The multi-Fano interference, which is obtained through the simultaneous acquisition of bright and dark states in different phase transitions of Eu³⁺ : BiPO₄ (7 : 1, 6 : 1, 1 : 1, and 0.5 : 1) and Eu³⁺ : NaYF₄ (1 : 1/4) crystals, were reported in this work. Multidressed spontaneous four-wave mixing and multidressed fluorescence (multiorder) were adopted to optimize the strong photon–phonon nested dressing effect, which results in more obvious multi-Fano interference. Firstly, the multi-Fano is produced through interference in continuous and multibound states. Secondly, five multi-Fano dips are originated from the nested five dressings (one photon and four phonons) under symmetrical splitting of ⁷F₁ energy level. It is found that the pure H-phase (0.5 : 1) sample exhibits the strongest photon–phonon dressed effect (five Fano dips). Further, high-order non-Hermitian exceptional points in multi-Fano interference were investigated by adjusting the ratio of Rabi frequency to dephase rate through nested photon and phonon dressing. The experimental results are validated by theoretical simulations, which may be applied to designing optoelectronic devices such as non-Hermitian multi-Fano interferences (multichannel) router.