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arXiv:cond-mat/0602504 · New Journal of Physics

Disorder-enhanced phase coherence in trapped bosons on optical lattices

Pinaki Sengupta, Aditya Raghavan, Stephan Haas

Published Apr 25, 2007• 16 citations
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Abstract

The consequences of disorder on interacting bosons trapped in one-dimensional optical lattices are investigated by quantum Monte Carlo simulations. A numerical analysis of the momentum distribution function, the stiffness and the compressibility reveals a unique response to small to moderate strengths of potential disorder. If there is a Mott plateau at the centre of the trap in the clean limit, phase coherence increases as a result of disorder. The localization effects due to correlation and disorder compete against each other, resulting in a partial delocalization of the particles in the Mott region, which in turn leads to increased phase coherence. In the absence of a Mott plateau, this effect is absent. A detailed analysis of the uniform system without a trap shows that the disordered states participate in a Bose glass phase.

DOI
10.1088/1367-2630/9/4/103

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The consequences of disorder on interacting bosons trapped in one-dimensional optical lattices are investigated by quantum Monte Carlo simulations. A numerical analysis of the momentum distribution function, the stiffness and the compressibility reveals a unique response to small to moderate strengths of potential disorder. If there is a Mott plateau at the centre of the trap in the clean limit, phase coherence increases as a result of disorder. The localization effects due to correlation and disorder compete against each other, resulting in a partial delocalization of the particles in the Mott region, which in turn leads to increased phase coherence. In the absence of a Mott plateau, this effect is absent. A detailed analysis of the uniform system without a trap shows that the disordered states participate in a Bose glass phase.
We explore the consequences of disorder on phase coherence in the Mott insulator phases in an optical lattice. Few bosons with contact interaction in small optical lattice can feature varieties of insulating phases---weakly interacting Mott in deep lattice, maximally fragmented and strongly interacting Mott in intermediate lattice, weak Mott with double filling and intrawell coherence, fermionized Mott with strong intrawell coherence. Utilization of the multiconfigurational time-dependent Hartree method for bosons to solve the many-boson Schr\"odinger equation, facilitates to understand the microscopic effect of disorder on the different kinds of Mott phases in the primary lattice. The many-body properties are analyzed by distinct measures of the reduced one-body density in real and momentum space, fragmentation, order parameter, variance of spatial single-shot measurements, compressibility, and the Glauber normalized correlation functions. We find very complex competition of localization due to disorder and Mott correlation. We observe distinct response of four different Mott phases in the disordered lattice. When the weakly interacting Mott exhibits the Bose glass phase, the strongly correlated and fully fragmented Mott exhibits leakage, melting and central localization. In contrast, weak Mott with double filling which is a spatially separated dimer in each site, exhibits only some dissociation of intrawell coherence and assist in the development of interwell coherence in the presence of strong disorder. For the fermionized Mott, when the density in each well is fragmented, strong disorder interferes with the intrawell correlation and the characteristic dip in each site starts to disappear leading to simple Mott localization with a pair of bosons.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.
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.
We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.