the host lattice. The dephasing of state is especially important; ideally should be a robust, metastable state. Currently EIT research uses atomic systems in dilute gases, solid solutions, or more exotic states such as Bose–Einstein condensate. EIT has been demonstrated in electromechanical and optomechanical systems, where it is known as optomechanically induced transparency. Work is also being done in semiconductor nanostructures such as quantum wells, quantum wires and quantum dots. Theory EIT was first proposed theoretically by professor Jakob Khanin and graduate student Olga Kocharovskaya at Gorky State University (renamed to Nizhny Novgorod in 1990), Russia; there are now several different approaches to a theoretical treatment of EIT. One approach is to extend the density matrix treatment used to derive Rabi oscillation of a two-state, single field system. In this picture the probability amplitude for the system to transfer between states can interfere destructively, preventing absorption. In this context, "interference" refers to interference between quantum events (transitions) and not optical interference of any kind. As a specific example, consider the lambda scheme shown above. Absorption of the probe is defined by transition from to . The fields can drive population from - directly or from ---. The probability amplitudes for the different paths interfere destructively. If has a comparatively long lifetime, then the result will be a transparent window completely inside of the - absorption line. Another approach is the "dressed state" picture, wherein the system + coupling field Hamiltonian is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination of Autler-Townes splitting and Fano interference between the dressed states. Between the doublet peaks, in the center of the transparency window, the quantum probability amplitudes for the probe to cause a transition to either state cancel. A polariton picture is particularly important in describing stopped light schemes. Here, the photons of the probe are coherently "transformed" into "dark state polaritons" which are excitations of the medium. These excitations exist (or can be "stored") for a length of time dependent only on the dephasing rates. Slow light and stopped light It is important to realize that EIT is only one of many diverse mechanisms which can produce slow light. The Kramers–Kronig relations dictate that a change in absorption (or gain) over a narrow spectral range must be accompanied by a change in refractive index over a similarly narrow region. This