Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

Lüschen, Henrik P.; Scherg, Sebastian; Kohlert, Thomas; Schreiber, Michael; Bordia, Pranjal; Li, Xiao; Sarma, S. Das; Bloch, Immanuel

doi:10.1103/physrevlett.120.160404

Cited by 292 publications

(215 citation statements)

References 42 publications

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“…In presence of a mobility edge, there is a coexistence of both kinds of behaviors due to presence of both localized and delocalized states. This has recently been seen in experiment [36].…”

supporting

confidence: 68%

“…Even though the AAH model has no mobility edge, various generalizations of it, as well as other quasiperiodic systems, have been shown to have mobility edges in one dimension. Recently, physics of such systems have attracted a lot of attention [23][24][25][26][27][28][29][30][31][32][33][34][35] and has also been experimentally realized [36]. In this paper, we focus on one such model that has been recently proposed [23][24][25][26][27].…”

mentioning

confidence: 99%

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Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

2017

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We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-André-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current, calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a 'critical' line separating regions of ballistic and localized transport. Like the critical point of AAH model, current scales sub-diffusively with system size on the 'critical' line (I ∼ N −2±0.1 ). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where I ∼ N −1.4±0.05 ). All these results can be understood from the above-mentioned connection between states near mobility edge of GAAH model and those of critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.Introduction: Anderson localization is a phenomenon seen in a wide class of systems [1][2][3]. It refers to spatial localization of energy eigenstates in the presence of uncorrelated disorder and in absence of interactions. In one and two dimensions, even a small amount of disorder makes all energy eigenstates localized. In three dimensions, beyond a critical strength of disorder, there occurs a mobility edge [4] separating localized and extended eigenstates. Understanding the physics of such a three dimensional system from a microscopic model is difficult. As a result, it is of interest to develop and study, theoretically and experimentally, lower dimensional models with a mobility edge.

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“…In presence of a mobility edge, there is a coexistence of both kinds of behaviors due to presence of both localized and delocalized states. This has recently been seen in experiment [36].…”

supporting

confidence: 68%

mentioning

confidence: 99%

Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

2017

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“…Recently, two articles have been made available exploring the SPMEs [44] that appear naturally due to NNN tunneling in weak real-space optical lattices featuring AA disorder [45] and exploring the interplay of disorder and artificial gauge fields in kicked rotor systems [46].…”

Section: Discussionmentioning

confidence: 99%

Engineering a Flux-Dependent Mobility Edge in Disordered Zigzag Chains

2018

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There has been great interest in experimental studies of charged particles in artificial gauge fields. Here, we perform the first cold-atom explorations of the combination of artificial gauge fields and disorder. Using synthetic lattice techniques based on parametrically coupled atomic momentum states, we engineer zigzag chains with a tunable homogeneous flux. The breaking of time-reversal symmetry by the applied flux leads to analogs of spin-orbit coupling and spin-momentum locking, which we observe directly through the chiral dynamics of atoms initialized to single lattice sites. We additionally introduce precisely controlled disorder in the site-energy landscape, allowing us to explore the interplay of disorder and large effective magnetic fields. The combination of correlated disorder and controlled intrarow and interrow tunneling in this system naturally supports energy-dependent localization, relating to a single-particle mobility edge. We measure the localization properties of the extremal eigenstates of this system, the ground state and the most-excited state, and demonstrate clear evidence for a flux-dependent mobility edge. These measurements constitute the first direct evidence for energy-dependent localization in a lower-dimensional system, as well as the first explorations of the combined influence of artificial gauge fields and engineered disorder. Moreover, we provide direct evidence for interaction shifts of the localization transitions for both low-and high-energy eigenstates in correlated disorder, relating to the presence of a many-body mobility edge. The unique combination of strong interactions, controlled disorder, and tunable artificial gauge fields present in this synthetic lattice system should enable myriad explorations into intriguing correlated transport phenomena.

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“…One can obtain a one-dimensional model displaying the mobility edge when the so-called self-dual symmetry is broken, such as a system with a shallow one-dimensional quasi-periodic potential [47][48][49][50][51]. Another class of systems with the mobility edge by introducing a long-range hopping term [31] or a special form of the on-site incommensurate potential [52] present the energy-dependent self-duality in the compactly analytic form.…”

Section: Introductionmentioning

confidence: 99%

“…Experimentally, the observation of the mobility edge has been reported in non-interacting ultra-cold atomic systems with a three-dimensional speckle disorder [11][12][13][14] and different numerical methods are proposed to estimate the position of E c [14,[84][85][86][87][88]. By monitoring the time evolution of the density imbalance and the global size of the atom cloud, the direct experimental research of the mobility edge in a one-dimensional quasi-random optical lattice of an initial charge-density wave state [47] is in good agreement with the theoretical results [89].…”

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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Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

Cited by 292 publications

References 42 publications

Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

Engineering a Flux-Dependent Mobility Edge in Disordered Zigzag Chains

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

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