Localization in momentum space of ultracold atoms in incommensurate lattices

Larcher, Marco; Modugno, Michèle; Dalfovo, F.

doi:10.1103/physreva.83.013624

Cited by 22 publications

(12 citation statements)

References 22 publications

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“…This interesting property attracts much attention and extensive theoretical and experimental studies of disorder effects in quantum systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Recently, due to the advances in manipulation of ultra-cold atoms, some experiments have realized the quasi-periodic model in optical lattices and observed the localization transitions [19,20].…”

Section: Introductionmentioning

confidence: 97%

Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

Liu

2015

Int J Theor Phys

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The concept of quantum Fisher information (QFI) is used to characterize the localization transitions in three representative one-dimensional models. It is found that the localization transition in each model can be distinctively illustrated by the evolution of QFI. For the Aubry-André model, the QFI exhibits an inflexion at the boundary between the extended states and localized ones. In the t 1 − t 2 model, the QFI has a transition point separating the extended states from the localized states, while the mobility edge of the QFI is energy dependent. Furthermore, nine energy bands in the Soukoulis-Economou (S-E) model can be clearly revealed by the QFI with global mobility edges and local mobility edges. The present work demonstrates the implication of the QFI as a general fingerprint to characterize the localization transitions.

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Section: Introductionmentioning

confidence: 97%

Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

Liu

2015

Int J Theor Phys

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“…One demonstrates that due to the self-duality characteristic [22], all the eigenstates are extended or localized, which depends on the parameters of the system [23], and there exist no mobility edges. Involved phenomena in the Aubry-André (AA) model have been investigated, such as Hofstadter's butterfly [24,25], metal-insulator transition [26][27][28][29][30][31][32][33][34][35][36], topologically nontrivial properties [37][38][39][40][41][42] and many body localization [43][44][45][46], etc.…”

Section: Introductionmentioning

confidence: 99%

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

Huangfu

Zhang

et al. 2020

New J. Phys.

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We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system.

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“…Indeed the role of a 1D OL, such as the BCOL [10,11], and in conjunction with atom-atom interactions in defining the properties of confined bosons lies at the heart of many investigations today [12,17,[19][20][21][22][23]. So far, the BCOL has been mostly applied to introduce quasidisorder in a "common experimental route" [12].…”

Section: Introductionmentioning

confidence: 99%

“…So far, the BCOL has been mostly applied to introduce quasidisorder in a "common experimental route" [12]. This is usually achieved by superimposing two OL wavelengths whose ratio λ 1 /λ 2 yields an irrational number [19,21,22]. However, the lattice setup with a rational number λ 1 /λ 2 is not very common and deserves therefore an investigation, particularly due to the likelihood that there may be not much difference between the use of a rational and irrational λ 1 /λ 2 .…”

Section: Introductionmentioning

confidence: 99%

Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

Sakhel

2016

Phys. Rev. A

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The sensitivity of the Sine-Gordon (SG) transition of strongly interacting bosons confined in a shallow, one-dimensional (1D), periodic optical lattice (OL), is examined against perturbations of the OL. The SG transition has been recently realized experimentally by Haller et al. [Nature 466, 597 (2010)] and is the exact opposite of the superfluid (SF) to Mott insulator (MI) transition in a deep OL with weakly interacting bosons. The continuous-space worm algorithm (WA) Monte Carlo method [Boninsegni et al., Phys. Rev. E 74, 036701 (2006)] is applied for the present examination. It is found that the WA is able to reproduce the SG transition which is another manifestation of the power of continuous-space WA methods in capturing the physics of phase transitions. In order to examine the sensitivity of the SG transition, it is tweaked by the addition of the secondary OL. The resulting bichromatic optical lattice (BCOL) is considered with a rational ratio of the constituting wavelengths λ1 and λ2 in contrast to the commonly used irrational ratio. For a weak BCOL, it is chiefly demonstrated that this transition is robust against the introduction of a weaker, secondary OL. The system is explored numerically by scanning its properties in a range of the Lieb-Liniger interaction parameter γ in the regime of the SG transition. It is argued that there should not be much difference in the results between those due to an irrational ratio λ1/λ2 and due to a rational approximation of the latter, bringing this in line with a recent statement by Boéris et al. [Phys. Rev. A 93, 011601(R) (2016)]. The correlation function, Matsubara Green's function (MGF), and the single-particle density matrix do not respond to changes in the depth of the secondary OL V1. For a stronger BCOL, however, a response is observed because of changes in V1. In the regime where the bosons are fermionized, the MGF reveals that hole excitations are favored over particle excitatons manifesting that holes in the SG regime play an important role in the response of properties to changes in γ.

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Localization in momentum space of ultracold atoms in incommensurate lattices

Cited by 22 publications

References 22 publications

Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

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