Giant Goos-Hänchen shift in two different enantiomers' chiral molecules via quantum coherence.

The Goos and Hänchen (GH) shifts in reflected and transmitted probe light through a cavity mixture of left- and right-handed chiral molecules into two enantiomer states are investigated. Due to the broken mirror symmetry of the left- and right-handed chiral molecules in the presence of cyclic population transfer, such quantum systems can be selectively excited because of the coexistence of one- and two-photon transitions. With the help of coupling Rabi frequency and damping effects due to scattering processes, the generated GH shifts accompanied by simultaneously negative and positive lateral shifts in reflected and transmitted probe lights are greatly enhanced. It is found that the large negative and positive GH shifts are available in the presence of multiphoton resonance and off-resonance conditions for two different enantiomers' chiral molecules. Moreover, the switching between superluminal and subluminal light propagation is extremely dependent on choosing the left- and right-handed chiral molecules. Furthermore, the effects of pulse shape and mode of Laguerre-Gaussian probe light on the GH shifts that lead to a switch between negative and positive shift are also studied. The negative and positive GH shifts in a reflected and transmitted probe beam for an incident Gaussian and different mode of Laguerre-Gaussian shaped beam with various widths by the use of two different enantiomers' chiral molecules are also discussed.