Gap solitons in Bose–Einstein condensate loaded in a honeycomb optical lattice: Nonlinear dynamical stability, tunneling, and self-trapping

2021 ◽  
pp. 126087
Author(s):  
Hongjuan Meng ◽  
Yushan Zhou ◽  
Xiaolin Li ◽  
Xueping Ren ◽  
Xiaohuan Wan ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Einstein Condensate ◽  
Dynamical Stability ◽  
Nonlinear Dynamical ◽  
Bose Einstein Condensate ◽  
Self Trapping ◽  
Gap Solitons ◽  
Bose Einstein

ON THE ENERGY OF A BOSE–EINSTEIN CONDENSATE IN AN OPTICAL LATTICE

2007 ◽  
Vol 19 (04) ◽  
pp. 371-384 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Optical Lattice ◽  
Critical Case ◽  
Periodic Potential ◽  
Einstein Condensate ◽  
Gamma Convergence ◽  
The Third ◽  
Bose Einstein Condensate ◽  
Delta Functions ◽  
Convergence Type ◽  
Bose Einstein

In this paper, we study the Gross–Pitaevskii energy of a Bose–Einstein condensate in the presence of an optical lattice, modeled by a periodic potential V(x3) in the third direction. We study a simple case where the wells of the potential V correspond to regions where V vanishes, and are separated by small intervals of size δ where V is large. According to the intensity of V, we determine the limiting energy as δ tends to 0. In the critical case, the periodic potential approaches a sum of delta functions and the limiting energy has a contribution due to the value of the wave function between the wells. The proof relies on Gamma convergence type techniques.

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