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arXiv:2410.13066 · Physical review. B./Physical review. B

Strongly interacting bosons in a one-dimensional disordered lattice: Phase coherence of distorted Mott phases

Barnali Chakrabarti, A. Gammal, Luca Salasnich

Published Nov 6, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.110.184202

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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.
Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator, and fermionized Tonks gases can be probed in such systems. To detect these phases---pivotal for both experiment and theory---as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground state for lattices with commensurate filling (i.e., an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases---the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by many-body entropy measures and by Glauber's normalized correlation functions. In sharp contrast, single-particle entropy cannot capture these phases.
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
We explore the effect of disorder on a few-boson system in a finite one-dimensional quasiperiodic potential covering the full interaction ranging from uncorrelated to strongly correlated particles. We apply numerically exact multiconfigurational time-dependent Hartree for bosons to obtain the few-body emergent states in a finite lattice for both commensurate and incommensurate filling factors. The detailed characterization is done by the measures of one- and two-body correlations, fragmentation, order parameter. For commensurate filling, we trace the conventional fingerprints of disorder induced localization in the weakly interacting limit, however we observe robustness of fragmented and strongly correlated Mott in the disordered lattice. For filling factor smaller than one, we observe existing delocalization fraction of particles interplay in a complex way. For strongly interacting limit, the introduced disorder drags the fragmented superfluid of primary lattice to Mott localization. For filling factor larger than one in the primary lattice, the extra delocalization always resides on commensurate background of Mott-insulator. We observe beyond Bose-Hubbard physics in the fermionization limit when the pairing bosons fragment into two orbitals -- Mott dimerization happens. The introduced disorder first relocates the dimers, then strong disorder starts to interfere with the background Mott correlation. These findings unlock a rich landscape of unexplored localization process in the quasiperiodic potentials and pave the way for engineering exotic quantum many-body states with ultracold atoms.
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 study distinctive features of local Mott insulator of trapped Bose-Fermi mixture systems on an optical lattice by using Monte-Carlo simulations of one-dimensional Bose-Fermi-Hubbard model. It was found that each species of the bosons and the fermions in a Mott insulator state had a finite stiffness but the density correlation function exhibited a quasi-long-range-order. This strongly suggested that in actual experiments the bosons and fermions of a commensurate filling with the lattice sites would form a Mott insulator state under strong interatomic interactions and have an order in their positional configuration.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.