Temporal and spectral hybrid bound state in continuum and its reliance on the correlation.

We study the hybrid bound states in continuum (BIC) in time and spectral domain obtained from Eu 3+ /Pr 3+ doped YPO 4 and BiPO 4 crystals. The spectral and time domain BIC originates from the interference between broadband fluorescence (FL) and narrowband super-florescence (SP-FWM) due to the dressing effect and crystal phase transition. We present a relationship between BIC and correlation and investigate two-mode and three-mode noise correlation/squeezing when the wavelength of the applied field is fixed at the bright state and dark state. In contrast to the BIC peak, we observe a switch and anti-bunching-like phenomenon at the BIC dip. We realize at the BIC peak point that correlation exhibits multi-oscillations and long coherence time in Pr 3+ :YPO 4 in contrast with Eu 3+ :YPO 4 . Further, our two-mode intensity noise correlation experimental results suggest a controllable bandstop filter with an 80% bandwidth contrast and a dual-channel amplifier with an 89% amplitude contrast.