Tunable photothermal and optomechanical transparency in a dual Bose-Einstein condensate hybrid system

We theoretically study photothermally and optomechanically induced transparency in a hybrid system of two coupled Fabry-Peŕot cavities. The left cavity hosts a dual-species Bose-Einstein condensate driven by pump and probe fields, while the right cavity couples to a mechanical resonator via photothermal effects. By tuning intercavity, optomechanical, and condensate-cavity couplings, both single and multiple transparency windows emerge. Interspecies and intraspecies interactions, along with effective coupling parameters, govern the transparency conditions, while the photothermal coefficient shapes the profiles. Absorption and dispersion spectra reveal that strong coupling enhances slow-light effects and group delay. These findings provide insights into tunable light-matter interactions for optical communication and photonic applications.