2004/05/17 by Hidetsugu Sakaguchi, H. Sakaguchi, Boris A. Malomed +1
Physics and Astronomy · #Atomic physics #Bose–Einstein condensate #Bound state #Brillouin zone #Center of mass (relativistic) #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Lattice (music) #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Soliton #Strong Light-Matter Interactions #Trapping #Vortex #Vorticity #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/0953-4075/37/11/001
17 pages, 12 figures
arxiv created 2004/05/17 · openalex publication_date 2004/05/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the dynamics of nonlinear localized excitations ('solitons') in two-dimensional (2D) Bose–Einstein condensates (BECs) with repulsive interactions, loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that a broad ('loosely bound', LB) soliton state, based on a 2D Bloch function near the edge of the Brillouin zone (BZ), has a negative effective mass (while the mass of a localized state is positive near the BZ centre). The negative-mass soliton cannot be held by the usual trap, but it is safely confined by an inverted parabolic potential ( anti-trap ). Direct simulations demonstrate that the LB solitons (including those with intrinsic vorticity) are stable and can freely move on top of the OL. The frequency of the elliptic motion of the LB-soliton's centre in the anti-trapping potential is very close to the analytical prediction which treats the solition as a quasi-particle. In addition, the LB soliton of the vortex type features real rotation around its centre. We also find an abrupt transition, which occurs with the increase of the number of atoms, from the negative-mass LB states to tightly bound (TB) solitons. An estimate demonstrates that for the zero-vorticity states, the transition occurs when the number of atoms attains a critical number N cr ∼ 10 3 , while for the vortex the transition takes place at N cr ∼ 5 × 10 3 atoms. The positive-mass LB states constructed near the BZ centre (including vortices) can also move freely. The effects predicted for BECs also apply to optical spatial solitons in bulk photonic crystals.