Abstract
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 $\ensuremath{\Lambda}$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\ensuremath{\Omega}}_{\ensuremath{\mu}}$, 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 interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow 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 interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by $g$. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.
Highlights
Induced transparencyEIT ͓1͔ is a quantum interference effect that occurs in coherently prepared three-level ⌳ atomic systems
The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ⍀, as in standard EIT systems
The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow 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 interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling
Summary
Induced transparencyEIT ͓1͔ is a quantum interference effect that occurs in coherently prepared three-level ⌳ atomic systems. We describe a modification of the standard three-level EIT configuration that utilizes coherent tunneling of a BEC in a double-well potential and leads to qualitative changes in the linear susceptibility of the probe laser, which, as a result, provides additional control over the absorption and dispersion. The additional control of the dispersion offered by the interwell tunneling holds the potential for being able to further manipulate the group velocity of light and four-wave mixing processes These results show that EIT can be an important diagnostic tool for BEC’s in double-well and periodic potentials since the linear absorption and index of refraction of the probe would provide a sensitive measure of the interwell coupling constants. The general form of the analytic solution is quite complicated and is given in Appendix B
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