  We investigate electromagnetically induced transparencies with two transverse
Bose-Einstein condensates in four-mirror optical cavity, driven by a strong
pump laser and a weak probe laser. The cavity mode, after getting split from
beam splitter, interacts with two independent Bose-Einstein Condensates
transversely trapped in the arms of the cavity along $x$-axis and $y$-axis. The
interaction of intra-cavity optical mode excites momentum side modes in
Bose-Einstein Condensates, which then mimic as two atomic mirrors coupled
through cavity field. We show that the probe field photons transition through
the atomic mirrors yields to two coupled electromagnetically induced
transparency windows, which only exist when both atomic states are coupled with
the cavity. Further, the strength of these novel electromagnetically induced
transparencies gets increased with an increase in atom-cavity coupling.
Furthermore, we investigate the behavior of Fano resonances and dynamics of
fast and slow light. We illustrate that the Fano line shapes and dynamics of
slow light can be enhanced by strengthening the interaction between atomic
states and cavity mode. Our findings not only contribute to the quantum
nonlinear optics of complex systems but also provide a platform to test
multi-dimensional atomic states in a single system.
