Direct observation of Anderson localization of matter waves in a controlled disorder
Direct observation of Anderson localization of matter waves in a controlled disorder
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DOI：
10.1038/nature07000
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发表时间：
2008-06-12
期刊：
影响因子：
64.8
通讯作者：
Aspect, Alain
中科院分区：
文献类型：
--
作者：
Billy, Juliette;Josse, Vincent;Aspect, Alain
1958年，安德森预言了无序晶体中电子波函数的局域化（1）以及由此导致的无扩散。现在人们认识到，安德森局部化在波动物理学中无处不在（2），因为它起源于多个散射路径之间的干涉。在实验上，光波（3-7），微波（8，9），声波（10）和电子气（11）的局域化已经被报道。然而，还没有直接观察到任何类型的物质波的指数空间局域化。在这里，我们观察到在存在由激光散斑产生的受控无序的情况下，释放到一维波导中的玻色爱因斯坦凝聚体的指数局域化（12）。我们在纯安德森局域化的状态下工作，也就是说，有弱无序--这样局域化是由许多低振幅的量子反射引起的--原子密度低到足以使相互作用忽略不计。我们直接将原子密度分布成像为时间的函数，发现弱无序可以阻止膨胀，并导致形成一个稳定的、指数定域的波函数--这是安德森定域的直接特征。我们提取的本地化长度拟合指数翼的配置文件，并比较它的理论计算。一维散斑势的功率谱具有高的空间频率截止，仅当膨胀凝聚体中原子的布罗意波长大于对应于该截止的有效迁移率边缘时才发生指数局域化。在相反的情况下，我们发现密度分布代数衰减，如参考文献13所预测的。本文提出的方法可以推广到更高维度的原子量子气体的局域化，并具有受控的相互作用。
In 1958, Anderson predicted the localization(1) of electronic wave-functions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics(2) because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves(3-7), microwaves(8,9), sound waves(10) and electron gases(11). However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose Einstein condensate released into a one- dimensional waveguide in the presence of a controlled disorder created by laser speckle(12). We operate in a regime of pure Anderson localization, that is, with weak disorder - such that localization results from many quantum reflections of low amplitude - and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction - a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one- dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.