Probing temperature and damping rates in Bose-Einstein condensates through dephasing in electromagnetically induced transparency conditions

We propose a method to probe Landau and Beliaev processes in dilute trapped atomic condensates with a multiple-state structure using electromagnetically induced transparency configurations. Under certain conditions, damping rates from these collisional processes are directly proportional to the dephasing rates, making it possible to determine damping rates through measurement of the dephasing. In the systems we consider, Landau decay rates are enhanced at low momenta, which allows one to distinguish between Landau-dominated and Beliaev-dominated regimes at the same temperature. Furthermore, the enhancement of Landau rates potentially provides a way to measure low temperatures (T⪡T_c) in dilute condensates more accurately than current methods permit.