Manipulating Transition And Entanglement Of A Laser-Kicked Two-Component Bose-Einstein Condensate

With the experimental realization of the Bose-Einstein condensation(BEC)in 1995, many researchers are devoted into this new field and have a well understood about it after two decades. This new state of matter have a low momentum and a long coherence length which make it easy for us to catch and manipulate the atoms. On that account, many manipulation schemes have been proposed.But the application on some new area like the quantum information and quantum computation bring a higher request on our manipulation,especially the manipulation speed. Because it request a time scale smaller than the de-coherence time.With the development of the laser technology, people start to use an ultrafast laser pulse to manipulate atoms which can reduce the operation time to several ps. In this paper, we apply this ultrafast laser to a many body BEC system and try to manipulate the transition and entanglement dynamics of it aimed to reduce the manipulation time.The full text consists of four chapters, The first chapter give a brief introduce of the BEC and introduce a quantum kicked top model which is famous in kicked system, and a many-body entanglement states in BEC.In chapter two, we study the dynamics of a kicked two-level BEC system specifically. Through a quantum perturbation method, we get the analytical solution of the transition probability in the angular momentum representation. We found the transition probability show an oscillating behavior in general and remain small. The interesting part is that there exist a single resonance case and a double resonance case. In the resonance case the transition probability will keep increase along with the laser kicks. Rely on this phenomenon, we proposed a scheme to transporting atoms between two internal states and a scheme to generate a many-body entanglement states by adjusting the pulse separation or the two-body interaction.In chapter three, we add a periodic drive on the kicked system and study the differences it brings. Firstly, we obtain the quasi-energy through a Floquet method and we found that this quasi-energy become virtual sometimes which correspond to a unstable state. Then we study the stability condition making the energy real. From the quasi-energy spectrum, we found the energy will change between degenerate and non-degenerate when the energy bias adds and found the degeneracy point. Finally, we study the transition properties of this system.In chapter four, a final summarize and a brief application prospect about the ultrafast manipulation are made.