Temperature variation of ultraslow light in a cold gas

Summary form only given. In the context of Bose-Einstein condensation in atomic gases, the scattering of light from a cold gas is an open front of investigation, both on the theoretical and experimental side. As much as it regards the propagation of radiation inside a cold gas, it is well known that the transmission of resonant light is almost zero. However, electromagnetic induced transparency has been proved to allow the propagation of a light pulse by means of quantum coherence between different internal atomic levels. In this context L.V. Hau et al. (1999) discovered a remarkable property of pulse propagation in a Bose condensate. These authors demonstrated the slowing down of the group velocity of the pulse to 17 m/sec and shown a definite dependence of the group velocity on the temperature of the cold sample. We develop a model based on approximate but plausible arguments to explain these observations. We solve the Maxwell-Bloch equations for a gas of non-interacting bosons initially in thermal equilibrium and derive an analytic expression for the group velocity of light in a cold gas for two cases: atoms confined in a box and by a harmonic potential. We obtain results which reproduce those of Hau et al. for temperatures above the critical value. In particular, the treatment brings out the factors playing the key role in the temperature dependence. We show that the variation of the spatial density of atoms with the temperature is the major factor responsible for the temperature dependence of the group velocity.