Coherent atomic states prepared by laser field can have quantum interference between the different transition amplitudes. Therefore, the medium susceptibility and optical response can be engineered, leading to many interesting phenomena, such as coherent population trapping (CPT), electromagnetically induced transparency (EIT), and lasing without inversion (LWI). We studied the coherence effects in various prototype atomic systems, and found many interesting applications. We solved the slow light bandwidth problem by decomposing the pulse and matching each frequency to its EIT window using a magnetic field gradient. We also considered the probe field deflection induced by the driving field distribution in EIT, and showed that even a broadband pulse can be deflected without serious spreading. In the fast light area, we examined the effects of noise and parameter deviations in a bichromatic Raman type white light cavity. Taking advantage of the adjustable absorption of EIT, we showed that EIT in a laser cavity can have either first-order or second-order phase transitions. Last but not least, we show that the adiabatic population transfer can be used to reverse the weak measurement of an arbitrary field with finite photon number.
