  Electromagnetically induced transparency (EIT) is an important tool for
controlling light propagation and nonlinear wave mixing in atomic gases with
potential applications ranging from quantum computing to table top tests of
general relativity. Here we consider EIT in an atomic Bose-Einstein Condensate
(BEC) trapped in a double well potential. A weak probe laser propagates through
one of the wells and interacts with atoms in a three-level $\Lambda$
configuration. The well through which the probe propagates is dressed by a
strong control laser with Rabi frequency $\Omega_{\mu}$, as in standard EIT
systems. Tunneling between the wells at the frequency $g$ provides a coherent
coupling between identical electronic states in the two wells, which leads to
the formation of inter-well dressed states. The tunneling in conjunction with
the macroscopic interwell coherence of the BEC wave function, results in the
formation of two ultra-narrow absorption resonances for the probe field that
are inside of the ordinary EIT transparency window. We show that these new
resonances can be interpreted in terms of the inter-well dressed states and the
formation of a novel type of dark state involving the control laser and the
inter-well tunneling. To either side of these ultra-narrow resonances there is
normal dispersion with very large slope controlled by $g$. For realistic values
of $g$, the large slope of this dispersion yields group velocities for the
probe field that are two orders of magnitude slower than standard EIT systems.
We discuss prospects for observing these ultra-narrow resonances and the
corresponding regions of high dispersion experimentally.
