Spectral and temporal atomic coherence interaction in Eu 3+  : NaYF 4 and Eu 3+  : BiPO 4 .

We investigate the spectral and temporal atomic coherence interaction based on out-of-phase fluorescence (FL) and spontaneous parametric four-wave mixing (SFWM) from the hexagonal phase of Eu 3+  : NaYF 4 and different phases of Eu 3+  : BiPO 4 . Spectral and temporal interactions are interrelated and reduced by about 2 times due to two-photon nested dressing in contrast to the sum of each laser excitation. As the lifetime of photons increases, off-resonance profile cross-interaction decreases because cross-interaction reverses the signal at the near time gate position and keeps it consistent at the far time gate position. Moreover, the thermal phonon dressing at 300 K exhibits 6 times more eminent and obvious temporal interaction than that at 77 K. In a different phase of Eu 3+  : BiPO 4 , there are three dark dips having stronger self-interaction; however, Eu 3+  : NaYF 4 has two dark dips as Eu 3+  : BiPO 4 has two phonon dressing. Further, the pure hexagonal phase of Eu 3+  : BiPO 4 demonstrates the strongest cross-interaction and longest coherent time under the dressing effect due to the smallest dressing phonon detuning and off-resonance profile cross-interaction at PMT2 because the angle quantization is the strongest. Such results can be used for designing novel quantum devices and have potential applications in quantum memory devices.