Anderson localization of matter waves

Abstract

The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization [1,2], percolation [3], disorderdriven quantum phase transitions and the corresponding Bose-glass [4] or spin-glass [5] phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. The basic knowledge is that contrary to Bloch's theory which predicts a (frictionless) transport of non-interacting particles [6] as a consequence of the extension of all eigenstates in a periodic crystal, localization effects in disordered potentials result in a strong suppression of the electronic transport in amorphous solids. In 1958, P.W. Anderson predicted the exponential localization [1] of electronic wave functions in disordered crystals and the resulting absence of diffusion. It has been realized later that Anderson localization (AL) is ubiquitous in wave physics [7] as it originates from the interference between multiple scattering paths and this has prompted an intense activity. Experimentally, localization has been reported in light waves [8], microwaves [9], sound waves [10] and electron gases [11]. Here we present the observation of Anderson localization [12, 13] of a Bose-Einstein condensate (BEC) released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle.In the experiment we observe the 1D Anderson Localization of an expanding BEC in presence of weak disorder potential created by laser speckle (Fig. 1). The 87 BEC is created in a hybrid optomagnetic trap [14] where the transverse confinement (ω ⊥ /2π = 70) is given by an optical wave guide (Nd:YAG laser at 1064 nm) whereas a weak magnetic gradient ensures the longitudinal trapping (ω z /2π = 5.4) (see Fig. 2). When the magnetic field is switched off, the BEC starts to expand along the optical guide under the effect of the initial interactions. In the early time of the expansion these interactions decrease rapidly and the associated energy is converted into kinetic one. We also show that, in our one-dimensional speckle potential whose noise spectrum has a high spatial frequency cut-off, exponential localization occurs only when the de Broglie wavelengths of the atoms in the expanding BEC are larger than an effective mobility edge corresponding to that cut-off. In the opposite case, we find that the density profiles decay algebraically [15].The random potential V is realized by focusing an optical speckle pattern, resulting from an Argon laser (w...

Transmission in waveguides with compositional and structural disorder: experimental effects of disorder cross-correlations

“…The theoretical predictions about the existence of delocalised states in 1D or quasi-1D models with correlated disorder [6,1,2,3,4] soon found experimental confirmations in semiconductor superlattices [7] and microwave waveguides [8,9]. Since these early works, 1D models with correlated disorder have found applications in an increasing number of physical fields, including Bose-Einstein condensates [10,11,12], bilayered media [13], structures with corrugated surfaces [14,15], and DNA modelling [16,17].…”