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Localization-Delocalization Transition in Ultracold Atomic Mixtures

Jean-François Schaff, Z. Akdeniz, Patrizia Vignolo

Published Oct 14, 2009• 0 citations
OpenAlex

Abstract

The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions, and without modifying the impurity correlations.

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The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions, and without modifying the impurity correlations.
The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions and without modifying the impurity correlations.
We introduce a two-dimensional short-range correlated disorder that is the natural generalization of the well-known one-dimensional dual random dimer model [D. H. Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)]. We demonstrate that, as in one dimension, this model induces a localization-delocalization transition in the single-particle spectrum. Moreover we show that the effect of such a disorder on a weakly interacting boson gas is to enhance the condensate spatial homogeneity and delocalization and to increase the condensate fraction around an effective resonance of the two-dimensional dual dimers. This study proves that short-range correlations of a disordered potential can enhance the quantum coherence of a weakly interacting many-body system.
Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper, we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First, we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-Andr\'e Hamiltonian and its modification including next-nearest-neighbor hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localization tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then, we investigate the effect of weak repulsive interactions in the Aubry-Andr\'e Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalization induced by interactions.
A one-dimensional interacting electron gas in a random potential exhibits a localized-delocalized transition for increasingly attractive interactions. We develop here a renormalization-group approach to study this transition. Our treatment allows us to obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and the strength of the interactions. For (nearly) spin-isotropic interactions the delocalized phase is dominated by superconducting fluctuations of either singlet or triplet type. The temperature dependence of the conductivity in the delocalized phase is also obtained and a nonuniversal power-law behavior is found. A description of the crossover towards the localized phase is given and the localization length is computed. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions. We suggest a phase diagram with two different localized phases. Finally, we discuss some possible implications of our model for real quasi-one-dimensional metals.
The possibility of using ultracold atoms to observe localization of matter waves is now a subject of significant interest. These systems offer unprecedented control over inter-particle interactions, imposed potentials and the level of disorder as compared to their condensed matter analogues. The two-dimensional (2D) case is of particular interest. The prevailing view has been that in the 2D electron gas there is no metallic state, but recent experiments are suggestive of a metal-insulator transition in very dilute systems. We investigate theoretically the possibility of observing strongly localized states, corresponding to the insulating phase, in the dilute 2D gas.
We experimentally study one-dimensional, lattice-modulated Bose gases in the presence of an uncorrelated disorder potential formed by localized impurity atoms, and compare to the case of correlated quasidisorder formed by an incommensurate lattice. While the effects of the two disorder realizations are comparable deeply in the strongly interacting regime, both showing signatures of Bose-glass formation, we find a dramatic difference near the superfluid-to-insulator transition. In this transition region, we observe that random, uncorrelated disorder leads to a shift of the critical lattice depth for the breakdown of transport as opposed to the case of correlated quasidisorder, where no such shift is seen. Our findings, which are consistent with recent predictions for interacting bosons in one dimension, illustrate the important role of correlations in disordered atomic systems.