Artificial Gauge Field In The BEC

We devote to studying artificial gauge potential theory with the atom-molecule conversion system in the cold atom physics as background. The atom-molecule converision process we concerned is:atoms is are firstly prepared into Feshbach molecules via Feshbach resonance and then transferred through an in-termediate excited state to the absolute molecular ground state through two-photon Ramman process Ω1,Ω2-In the rotating wave approximation Hamito-nian of such process can be expressed as the sum of free partical Hamitonian and a coupling operater. When Feshbach resonance, atom binding energy, and detuning far less than atom-light coupling|Ω1|Ω2|,"dress" state of coupling operater have nearly degenerated dark state submanifold. From artificial gauge potential theory we know that when we project full Schrodinger equation in the dark state submanifold there where emergy a non-Abelian guage potential in the projecting (effective) Hamiltonian. In the laser field which is constructed by two counterpropagating and overlapping laser beams with shifted spatial profiles, we study wavepakage dynamics of such Hamiltonian. We observe spin Hall effect and do some quantum classical correspondence study. On the other hand, ef-fective Hamiltion will have different form in different basis of degenerated dark submanifold. And there is a basis which is formed by atomic state and the super-position of Feshbach molecular state and ground state moleculer state. In such basis study spin Hall effect, we find atom and molecule separate spacially. Since the superposition of Feshbach molecular state and ground state molecular state has different form at different place in the x direction, when wavepakage move in x direction there will be exchange between Feshbach molecule and ground state molecule. We call such process spatial Ramman process. From this point of view, we propose a scheme to getting ground state molecule. In our laser field, superposition state can be treated as Feshbach molecule state at the point which is far from x=0in the x<0range and as ground state molecule state at the point which is far from x=0in the x>0range. Our wavepakage is in the area which is far from x=0in the x<0range at beginning, moves in the gravity field and finally in the area which is far from x=0in the x<0range. In this process Feshbach molecule will change into ground state molecule. Considering an atomic BEC in harmonic potenitial using Feshbach resonance on such BEC, we can get our initial state. The remaining atoms can be separated from our ground state via spin Hall effect. Further more, we can set our intial state as the superposition of an atomic Gaussion wavepakage and a Feshbach molecule Gaussion wavepakage and study wavepakage dynamics without artifi-cial gauge potential approximation. We find that atoms and molecules separate spatially and Feshbach molecule changes into ground state molecule which proves our shceme can work. Finally we discuss how to make our shceme more efficient. Otherwise we brieftly discuss the condition for artificial potential approximation.