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

Quantum control of EIT dispersion via atomic tunneling in a double-well Bose-Einstein condensate