Co-manipulation Dynamics Of A Bose-Einstein Condensate And An Optical Field

Bose-Einstein condensate(BEC)has important applications in many fields such as quantum simulation,precision measurement and quantum information.In these researches,laser is a very important technique to manipulate BEC dynamics.The recent research shows that during the optical manipulatiuon,the BEC can have a feedback effect on the light field.This phenomenon is called local-field effect.Now,the optical properties of Bose-Einstein condensate as quantum dielectric materials have generated interest in quantum optics and ultra-cold atomic physics.According to this research trend of BEC,our thesis studies the interaction between the BEC and light.We first studied the dispersion relation of BEC for optical fields with a large detuning,analytically obtained the formulas for the first and the second order dispersion.Our numerical calculation shows that the refractive index and the second-order dispersion coefficient depends on the properties of red or blue detuning.In the case of red detuning,the value of refractive index greater than 1,and the second-order dispersion is normal dispersion.In the case of blue detuning,the value of refractive index less than 1,and the second-dispersion is anomalous dispersion.The second-order dispersion coefficient will change dramatically with the change of detuning.When the detuning quantity is in the order of GHz,the BEC can function as a strong dispersion medium.The first-order dispersion is independent with red detuning or blue detuning,and with the increase of the detuning,the first-order dispersion decreases,and the group velocity will increase accordingly.Our research shows that the BEC is a new dispersion medium for manipulating ultrashort pulse light.We further investigate the diffraction dynamics of a two-level BEC system by an optical lattice.we don't adopt the conventional adiabatic elimination of excited states in our numericla anlaysis,and find that the excited state leads to the diffraction fringes at odd number photon momentum,although their intensities are very weak due to the large detuning.We further compare our results with those obtained using the adiabatical elimination of excited states,and found that the influence of atomic interaction on adiabatic elimination is significant,especially when the order of magnitude of the detuning is about GHz.Finally,using the Cayley-Hamilton formula,we have developed a new algorithm to solve the modifed coupled-mode equation for the propagation of light in the onedimensional BEC.