Single-particle localization in dynamical potentials

Major, Jan; Morigi, Giovanna; Zakrzewski, Jakub

doi:10.1103/physreva.98.053633

Cited by 17 publications

(12 citation statements)

References 91 publications

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“…Here, β = k/k L is the ratio between k, the wavenumber of the cavity mode, and k L , the wavenumber corresponding to the optical lattice, and φ is a phase in the mode function. In our work we consider β = 1, and note that arbitrary values of β would lead to a quasiperiodic Hamiltonian [81,82]. For β = 1 and for i = j the magnitude of the integral becomes independent of i, that can be written as…”

Section: A Coefficients Of the Extended Bose-hubbard Modelmentioning

confidence: 99%

Self-organized topological insulator due to cavity-mediated correlated tunneling

Chanda

Kraus

Morigi

et al. 2021

Quantum

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Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings. Originating from quantum interference, this topological phase is found in "exact" density-matrix renormalization group calculations and is entirely absent in the mean-field approach. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.

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Section: A Coefficients Of the Extended Bose-hubbard Modelmentioning

confidence: 99%

Self-organized topological insulator due to cavity-mediated correlated tunneling

Chanda

Kraus

Morigi

et al. 2021

Quantum

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“…The IPR provides a well-behaved measure of how localized a particular state is [81]. Related to this, recent work has also examined the effect of 'dynamical localization' in dynamical optical lattice potentials [82]. In particular we wish to calculate For non-interacting spatially localized states, the IPR takes a value of one such that  = -( ) t 1 1 , while delocalized states are found instead when  - ( ) t 1 1 .…”

Section: Impurity Localization Transitionmentioning

confidence: 99%

Coherent impurity transport in an attractive binary Bose–Einstein condensate

2019

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We study the dynamics of a soliton-impurity system modeled in terms of a binary Bose-Einstein condensate. This is achieved by 'switching off' one of the two self-interaction scattering lengths, giving a two component system where the second component is trapped entirely by the presence of the first component. It is shown that this system possesses rich dynamics, including the identification of unusual 'weak' dimers that appear close to the zero inter-component scattering length. It is further found that this system supports quasi-stable trimers in regimes where the equivalent single-component gas does not, which is attributed to the presence of the impurity atoms which can dynamically tunnel between the solitons, and maintain the required phase differences that support the trimer state. that the single component focussing nonlinear Schrödinger equation can possess chaotic solutions in the presence of an axial harmonic potential [29,30], as well as the observed interaction induced frequency shift of pairs of trapped bright solitons [31] in the experiment of [13]. Complementary to this, theoretical work has focussed on solitary waves in higher spin systems, revealing the existance of integrable points in the full parameter space of the spin-1 condensate, in the form of so-called 'polar' bright solitons [32,33]. Although solitons are usually studied as the solutions to one-dimensional nonlinear models, there have also been predictions of stable two-dimensional solitary wave solutions in dipolar Bose-Einstein condensates [34,35], where the additional nonlocal nonlinearity provides the stabilizing mechanism for these solitons. Very recently the Jones-Roberts soliton was realized experimentally, a true two-dimensional solitary wave structure [36].The realization of artificial electromagnetism with cold gases, and in particular spin-orbit coupling for Bose-Einstein condensates opens a novel route towards studying nonlinear wave structures. Here, the coupling of the condensates momentum to a quasi-spin leads to stripe-like soliton phases, related to the underlying immiscible phase of these systems [37,38]. Spin-orbit coupling forms a key ingredient in simulating more exotic scenarios, such as Dirac-like equations, where confined solutions have been predicted [39] that resemble their bright soliton cousins in single component condensates.Atomic condensates benefit from being exceptionally pure systems-this in turn allows one to investigate the effects of disorder and defects with an unprecedented level of control. The presence of impurities in ensembles of ultracold matter has led to predictions of impurity-molecules and lattices at the mean-field level [40], as well as the role of many-body correlations for a single impurity out-of-equilibrium [41]. Experimental work has studied the role that spin impurities have in the strongly correlated Tonks-Girardeau limit [42] and also magnetic spin models [43], which have also been the focus of subsequent theoretical investigations [44][45][46]. Complementary to this, recent exper...

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“…[ 15,63 ] Furthermore, the paradigmatic AA model has been experimentally implemented in ultracold atoms loaded into bichromatic optical lattices [ 54,64–67 ] and coupled‐waveguide photonic crystals. [ 15,16,55,61 ] While the paradigmatic AA model violates the predictions of scaling theory [ 68 ] and displays the key traits of localization transitions commonly manifested by 3D systems with stochastic (uncorrelated) disorder, a more interesting and important phenomenon is the emergence of energy‐dependent mobility edges [ 69–85 ] when the paradigmatic AA model is elaborately tampered to break the self‐dual symmetry. Some such manipulations include the modifications of on‐site modulation [ 86,87 ] and the extensions of nearest‐neighbor hopping.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic Pumping in a Generalized Aubry–André Model Family with Mobility Edges

Xing

Zhao

et al. 2021

Annalen der Physik

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The adiabatic pumping between left and right end modes in a generalized Aubry–André model family with mobility edges by resorting to two end–bulk–end channels is investigated. It is shown that the system can be in an intermediate regime mixed with localized and extended phases as the mobility edge is introduced. One of the channels can remain intact even when the parameter determining the localization–delocalization transition exceeds the threshold of the paradigmatic Aubry–André model, leading to that the parametric condition for successful pumping is relaxed. Moreover, it is found that widening the region of the hybrid phase can further enhance the effect of the mobility edge. The pumping result is also quantified based on the fidelity and check the corresponding pumping process to validate these observations. Furthermore, another channel to realize a flexible adiabatic pumping among four types of generalized end modes is engineered. This work enables the potential application of mobility edges in strong–quasidisorder–immune quantum state transfer.

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Single-particle localization in dynamical potentials

Cited by 17 publications

References 91 publications

Self-organized topological insulator due to cavity-mediated correlated tunneling

Self-organized topological insulator due to cavity-mediated correlated tunneling

Coherent impurity transport in an attractive binary Bose–Einstein condensate

Adiabatic Pumping in a Generalized Aubry–André Model Family with Mobility Edges

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