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arXiv:1203.0505 · Physical Review B

Polar bosons in one-dimensional disordered optical lattices

Xiaolong Deng, R. Citro, E. Orignac, Anna Minguzzi, Luis Santos

Published May 2, 2013• 20 citations
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Abstract

We analyze the effects of disorder and quasidisorder on the ground-state properties of ultracold polar bosons in optical lattices. We show that the interplay between disorder and intersite interactions leads to rich phase diagrams. A uniform disorder leads to a Haldane-insulator phase with finite parity order, whereas the density-wave phase becomes a Bose glass at very weak disorder. For quasidisorder, the Haldane insulator connects with a gapped generalized incommensurate density wave without an intermediate critical region.

DOI
10.1103/physrevb.87.195101

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We analyze the effects of disorder and quasidisorder on the ground-state properties of ultracold polar bosons in optical lattices. We show that the interplay between disorder and intersite interactions leads to rich phase diagrams. A uniform disorder leads to a Haldane-insulator phase with finite parity order, whereas the density-wave phase becomes a Bose glass at very weak disorder. For quasidisorder, the Haldane insulator connects with a gapped generalized incommensurate density wave without an intermediate critical region.
Ultra cold polar bosons in a disordered lattice potential, described by the extended Bose–Hubbard model, display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases—the Mott-insulator and the Haldane insulator—in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential, further phases are found, e.g. the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.
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.
Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid-to-Bose-glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.
We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.
The influence of disorder on ultracold atomic Bose gases in optical lattices is discussed in the framework of the one-dimensional Bose–Hubbard model. It is shown that simple periodic modulations of the well depths generate a rich phase diagram consisting of superfluid, Mott insulator, Bose glass (BG) and spatially localized phases. The detailed evolution of mean occupation numbers and number fluctuations as function of modulation amplitude and interaction strength is discussed. Finally, the signatures of the different phases, especially of the BG phase, in matter–wave interference experiments are investigated.
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.