Controlling subluminal to superluminal behavior of group velocity in an   f-deformed Bose-Einstein condensate beyond the rotating wave approximation
  In this paper, we investigate tunable control of the group velocity of a weak probe field propagating through an f-deformed Bose-Einstein condensate of three-level atoms beyond the rotating wave approximation. For this purpose, we use an f- deformed generalization of an effective two-level quantum model of the three-level configuration without the rotating wave approximation in which the Gardiners phonon operators for Bose-Einstein condensate are deformed by an operator- valued function,f(n), of the particle- number operator n . Corrections produced by the counter- rotating terms appear in the first order as an intensity- dependent detuning and in the second order as an intensity- dependent atom-field coupling. We consider the collisions between the atoms as a special kind of f- deformation where the collision rate k is regarded as the deformation parameter. We demonstrate the enhanced effect of subluminal and superluminal propagation based on electromagnetically induced transparency and electromagnetically induced absorption, respectively. In particular, we find that (i) the absorptive and dispersive properties of the deformed condensate can be controlled effectively in the absence of the rotating wave approximation by changing the deformation parameter k, the total number of atoms N and the counter- rotating terms parameter, (ii) by increasing the values of k, 1/N and the counter- rotating terms parameter, the group velocity of the probe pulse changes, from subluminal to superluminal and (iii) beyond the rotating wave approximation, the subluminal and superluminal behaviors of the probe field are enhanced. 
Z. Haghshenasfard, M. Soltanolkotabi and M. H. Naderi