Bose-Einstein Condensation Project

• Collaborators(Theory): Prof. Qian Niu at Univ. of Texas at Austin.
• Here are preliminary results from the BEC calculation. Optical Lattice is turned on at t=0~2 and boosted to a final velocity 0.5 at t =30~35. Initial wavefunction is a Gaussian wavepacket. At the grid boundary, an annihilation boundary condition is used to "absorb" an outgoing component of the "wave". This condition has been used successfully in many cases. Magnitue of optical lattice V=0.1.
  
  
  
  • Currents (C=0,0.01,0.05,0.1,0.2,0.5) (Integrated over the whole computational domain=40 periods)
    Based on Run #1 right below.
    
    
    
  • Run #1 (Most RECENT one)
    X-domain spans 40 lattice periods (-40 pi ~ +40 pi)
    Initial Gaussian wave amp = 1
    Initial Gaussian wave width = 30 (about 9pi)
    Figures: show time evolution of wavefunction for C=0(Yellow/Red), wavefunction for C=0.1(Blue), and Optical Lattice(Purple). Time is indicatd by yellowish numbers at the upper left corners. Optical Lattice is dragged to the right.
    
    
    
    
  • Run #2: (Previous Run)
    X-domain spans 20 lattice periods (-20 pi ~ +20 pi)
    Initial Gaussian wave amp = 1
    Initial Gaussian wave width = 15 (about 9pi)
    MPEG FILESMovie (C=0.0) Movie (C=0.05) BLUE represents a dragged wavefuncion by an Optical Lattice (PURPLE). RED/YELLOW represents a reference wavefunction in a non-moving OL.
    
  • IF YOU CAN'T VIEW MPEG FILES, THE FOLLOWING IS THE SNAPSHOTS: BLUE represents a dragged wavefuncion by an Optical Lattice (PURPLE). RED/YELLOW represents a reference wavefunction in a non-moving OL.
    Time is indicatd by yellowish numbers at the upper left corners. Optical Lattice is dragged to the right.

    C=0.0
    

    
    

    C=0.05
    

    
  
  
  
• 3D BEC calculation
  
  • Test run with 3D BEC. Initial condition is a stationary BEC. Trap in longitudinal-direction is turned off at t=2 with transverse directions intact. Optical lattice is turned on instantaneously at t=2 (Well, should be changed for an adiabatic turn-on.) OL is given by [ V_0 * cos(k_l * z) ] where V_0=0.8 and k_l=2*pi and accelerated with accel=10 t>=2. C=0.0087
    You can see the steep gradient in BEC at ~ t=2.83. Only the front end of the BEC is dragged. After time>=3, the spreading of BEC starts to dominate the dynamics.(?)
    
    
    
    
    
    
    
    
• Discussion
  
  • Dragging of Gaussian wave packets by Optical Lattice was clearly demonstrated for both a non-interacting (C=0) and interacting BEC. For non-interacting case, BEC is dragged without much deformation. For the interacting case, BEC is deformed in a complicated way and only the initially low density region is dragged.??
    
  • Overall current is also reduced as the interaction ("C" term) is turned on as implied by the "screening" effect.
    
  • The nonlinearity ("C" term) contributes to "dispersion" of a wavepacket as well as screening effect and changes shape of Gaussian wave packet in a nontrivial way. This makes the analysis of the results difficult. This may also explain the "lump" at the trailing edge.??
    
  • Further analysis and calculation are underway.