Kumar S, Perego A M, Staliunas K
Departament de Fisica, Universitat Politècnica de Catalunya, E-08222, Barcelona, Spain.
Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom.
Phys Rev Lett. 2017 Jan 27;118(4):044103. doi: 10.1103/PhysRevLett.118.044103.
We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.
我们报道了在具有空间调制周期势的散焦区域（用于排斥性玻色 - 爱因斯坦凝聚体的格罗斯 - 皮塔耶夫斯基方程）中，非线性薛定谔方程的博戈留波夫 - 德热纳激发的聚焦情况。利用调制引起的色散关系的改变，我们证明了在博戈留波夫 - 德热纳激发的线性和非线性区域（线性和非线性“子弹”）中都存在局域结构。这些在共动参考系中在空间和时间上都局域化的行进博戈留波夫 - 德热纳子弹是稳健的，并且在传播过程中保持稳定，不会扩散或形成丝状。在由光学晶格诱导的空间周期势存在的情况下，本文报道的现象可以在原子玻色 - 爱因斯坦凝聚体中观察到。
