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arXiv:1003.3657 · Physical Review Letters

Quantum Correlations in Two-Particle Anderson Localization

Yoav Lahini, Yaron Bromberg, Demetrios N. Christodoulides, Yaron R. Silberberg

Published Oct 14, 2010• 179 citations
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Abstract

We predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.

DOI
10.1103/physrevlett.105.163905

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We predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.
Anderson localization – the halt of quantum transport in a strongly disordered potential – has been observed for quantum gases in optical potentials. An important stage of experiments is the creation and characterization of the optical (speckle) potential that typically features nontrivial correlations complicating the interpretation of measurements. We realize an alternative route towards Anderson localization of cold atoms using a mixture of two strongly mass-imbalanced atomic species without any externally imposed disordered potential. On short time scales, the heavy component can be considered immobile and creates a quasi-static scattering potential for the light component that experiences Anderson localization under appropriate conditions. Experimental results allow for a quantitative description based on the model of randomly distributed resonant point scatterers. This demonstrates an interesting and fruitful link between the phenomenon of (single-particle) Anderson localization and the so-called many-body localization that takes place in interacting quantum systems composed of many particles, which is the case of our experimental system.
We report a theoretical study of Anderson localization of nonclassical light with emphasis on the quantum statistical aspects of localized light. We demonstrate, from the variance in mean intensity of localized light, as well as site-to-site correlations, that the localized light carries signatures of quantum statistics of input light. For comparison, we also present results for input light with coherent field statistics and thermal field statistics. Our results show that there is an enhancement in fluctuations of localized light due to the medium's disorder. We also find superbunching of the localized light, which may be useful for enhancing the interaction between radiation and matter. Another important consequence of sub-Poissonian statistics of the incoming light is to quench the total fluctuations at the output. Finally, we compare the effects of Gaussian and Rectangular distributions for the disorder, and show that Gaussian disorder accelerates the localization of light.
We numerically explore the long-time expansion of a one-dimensional Bose-Einstein condensate in a disorder potential employing the Gross-Pitaevskii equation. The goal is to search for unique signatures of Anderson localization in the presence of particle-particle interactions. Using typical experimental parameters, we show that the time scale for which the nonequilibrium dynamics of the interacting system begins to diverge from the noninteracting system exceeds the observation times up to now accessible in the experiment. We find evidence that the long-time evolution of the wave packet is characterized by (sub)diffusive spreading and a growing effective localization length, suggesting that interactions destroy Anderson localization.
Anderson localization of waves in disordered media was originally predicted[1] fifty years ago, in the context of transport of electrons in crystals[2]. The phenomenon is much more general[3] and has been observed in a variety of systems, including light waves[4, 5]. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization[6]. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice - a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases[8, 9].
The interplay between disorder and topology triggers interesting effects for the propagation of quantum particles in low-dimensional network structures. For instance, the occurrence of Anderson localization, a commonly observed effect in a quantum network with static disorder, can be suppressed by introducing topology-a phenomenon dubbed as topological Anderson localization transition [1] . In one-dimensional systems, for example, disorder induces localization on a short length scale while topology counters that through long-range correlations, yielding divergent correlation length and extremely slow spreading at quantum criticality. However, its experimental demonstration still remains an outstanding challenge as that would require, in contrast to Anderson localization transition, addi¬tional control over internal degrees of freedom, which is hard to implement, for instance, in cold-atom systems [2] . Quantum walks (QWs), a quantum analog of random walks, comprising quantum coin toss and conditioned step operations are already established for studying quantum transport phenomena, such as, disorder and topology [5] . Based on our theoretical proposal [3] , here, we provide an experimental route using time-multiplexed quantum walk [4] for evidencing the targeted phenomenon.
We measure ensemble-averaged quantum correlations of path-entangled photons, propagating in a disordered lattice and undergoing Anderson localization. These result in intriguing patterns, which show that quantum interference leads to unexpected dependencies of the location of one particle on the location of the other. These correlations are shared between localized and nonlocalized components of the two-photon wave function, and, moreover, yield information regarding the nature of the disorder itself. Such effects cannot be reproduced with classical waves, and are undetectable without ensemble averaging.