Sanchez-Palencia L, Clément D, Lugan P, Bouyer P, Shlyapnikov G V, Aspect A
Laboratoire Charles Fabry de l'Institut d'Optique, CNRS and Univ. Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau cedex, France.
Phys Rev Lett. 2007 May 25;98(21):210401. doi: 10.1103/PhysRevLett.98.210401. Epub 2007 May 23.
We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k>1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)<sigma(R) it changes to algebraic.
我们表明，初始受限的相互作用一维玻色 - 爱因斯坦凝聚体的膨胀在具有关联长度σ(R)的弱随机势中可表现出安德森局域化。对于散斑势，当动量k > 2/σ(R)时，关联函数的傅里叶变换消失，以至于在玻恩近似中，当k > 1/σ(R)时李雅普诺夫指数消失。然后，对于凝聚体的初始愈合长度ξ(in) > σ(R)，局域化是指数型的，而当ξ(in) < σ(R)时，它变为代数型的。
