Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases

By G. Roux, Thomas Barthel, Ian P. McCulloch, C. Kollath, U. Schollwöck, Thierry Giamarchi. 2008

141 citations recorded by the source corpus.

We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasiperiodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical lattice in the presence of a superlattice potential whose wavelength is incommensurate with the main lattice wavelength. After discussing the conditions under which the model can be realized experimentally, the study of the density vs the chemical potential curves for a nontrapped system unveils the existence of gapped phases at incommensurate densities interpreted as incommensurate charge-density-wave phases. Furthermore, a localization transition is known to occur above a critical value of the potential depth V2 in the case of free and hard-core bosons. We extend these results to soft-core bosons for which the phase diagrams at fixed densities display new features compared with the phase diagrams known for random box distribution disorder. In particular, a direct transition from the superfluid phase to the Mott-insulating phase is found at finite V2. Evidence for reentrances of the superfluid phase upon increasing interactions is presented. We finally comment on different ways to probe the emergent quantum phases and most importantly, the existence of a critical value for the localization transition. The latter feature can be investigated by looking at the expansion of the cloud after releasing the trap.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/eb4e8693ff88764c8c694d39d3e3989dc3302f13

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

One dimensional bosons: From condensed matter systems to ultracold gases (2011, methodology): “DMRG approaches (Deng et al., 2008; Roux et al., 2008), combined with the above analytical considerations, allowed for a rather complete description of the physics of such quasi-periodic systems.”