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Register a new userThree-Dimensional Anderson Localization in Variable Scale Disorder
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We report on the impact of variable-scale disorder on 3D Anderson localization of a non-interacting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of four via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.
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Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential. A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component. We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy. These measurements provide a benchmark for more sophisticated theories of AL.
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization. The two-site approximation is solved analytically and shown to capture the essential features found in numerical simulations on one-, two- and three-dimensional systems. Further improvement has been obtained by solving a three-site model.
We show that a one dimensional disordered conductor with correlated disorder has an extended state and a Landauer resistance that is non-zero in the limit of infinite system size in contrast to the predictions of the scaling theory of Anderson localization. The delocalization transition is not related to any underlying symmetry of the model such as particle-hole symmetry. For a wire of finite length the effect manifests as a sharp transmission resonance that narrows as the length of the wire is increased. Experimental realizations and applications are discussed including the possibility of constructing a narrow band light filter.
We study the Anderson transition for three-dimensional (3D) $N times N times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy increases, for appropriately tailored disorder correlations. We predict the effect in one, two, and three dimensions, and propose a simple method to observe it using ultracold atoms placed in optical disorder. The increase of localization with the particle energy can serve to discriminate quantum versus classical localization.
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