Edge States and Topological Phases in One-Dimensional Optical Superlattices

Lang, Li-Jun; Cai, Xiaoming; Chen, Shu

doi:10.1103/physrevlett.108.220401

Cited by 311 publications

(355 citation statements)

References 38 publications

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“…It is well known that the Aubry-André model or the Aubry-André-Harper (AAH) model will shows a phase transition from extended states to localized states (Anderson localization) when the lattice is incommensurate [35][36][37][38]. The normal Hermitian AAH model with or without p-wave superconducting pairing presents abundant physical phenomena both in the commensurate and incommensurate situations [39][40][41][42][43][44][45][46][47][48][49][50][51]. However, the influences of physical gain and loss on the AAH model have not been explored much.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

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“…It can be intuitively seen that the population of the edge states both localize at the ends. They are the eigenstates of the natural Hamiltonian (3) with the protected eigenenergies [3]. We next show the procedure to prepare the 'm + 1' edge state by two kinds of Lyapunov control schemes.…”

Section: Fermionic Chain Made Of Atoms Loaded In Optical Latticementioning

confidence: 99%

“…Usually the topological character is indicated by the emergence of edge states for a bulk system. Recently, there have been a great deal of work to explore topological systems related to such states [2][3][4][5][6][7][8][9][10]. In two dimensional systems such as the Bi 2 Te 3 nanoribbon, manipulation of edge state by modulating a gate voltage has been reported in experiments [8].…”

Section: Introductionmentioning

confidence: 99%

Edge state preparation in a one-dimensional lattice by quantum Lyapunov control

Zhao¹,

Shi²,

Qin³

2016

J. Phys. B: At. Mol. Opt. Phys.

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Quantum Lyapunov control uses a feedback control methodology to determine control fields which are applied to control quantum systems in an open-loop way. In this work, we adopt two Lyapunov control schemes to prepare an edge state for a fermionic chain consisted of cold atoms loaded in an optical lattice. Such a chain can be described by the Harper model. Corresponding to the two schemes, state distance and state error Lyapunov functions are considered. The results show that both the schemes are effective to prepare the edge state within a wide range of parameters. We found that the edge state can be prepared with high fidelity even if there are moderate fluctuations in on-site or hopping potentials. Both control schemes can be extended to similar chains (3m + d, d=2) of different lengths. Since regular amplitude control field is easier to apply in practice, amplitudemodulated control fields are used to replace the unmodulated one to prepare the edge state. Such control approaches provide tools to explore edge states for one dimensional topological materials.

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“…The scheme as described, with local control over tunneling amplitudes and phases, permits the study of neararbitrary one-dimensional systems. Of natural interest would be the study of superlattice systems known to have non-trivial topological properties [8,[45][46][47][48], in particular when combined with either additional modulation of the tunneling parameters [49][50][51] or in the presence of disorder [52,53].…”

Section: E/ħ P/2ħkmentioning

confidence: 99%

Atom-optics approach to studying transport phenomena

Gadway

2015

Phys. Rev. A

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We present a simple experimental scheme, based on standard atom optics techniques, to design highly versatile model systems for the study of single particle quantum transport phenomena. The scheme is based on a discrete set of free-particle momentum states that are coupled via momentumchanging two-photon Bragg transitions, driven by pairs of interfering laser beams. In the effective lattice models that are accessible, this scheme allows for single-site detection, as well as site-resolved and dynamical control over all system parameters. We discuss two possible implementations, based on state-preserving Bragg transitions and on state-changing Raman transitions, which respectively allow for the study of nearly arbitrary single particle Abelian U(1) and non-Abelian U(2) lattice models. -for the quantum simulation of myriad physical phenomena, especially those related to condensed matter [4,5].For the study of single electron transport phenomena, photonic [6][7][8][9][10][11] and cold atom [12][13][14][15][16][17][18][19][20] simulators have made great progress in the experimental exploration of disordered and topological systems, while offering largely complementary capabilities and challenges. Photonic simulators generally permit control of system parameters and the detection of probability distributions at the microscopic, site-resolved level. However, the use of real materials as the medium for light transport makes these systems susceptible to inherent disorder in sample preparation [21] and to absorption in the material [22], and makes simulations in higher spatial dimensions and timedependent control of system parameters non-trivial. For cold atoms, pristine and dynamically variable potential landscapes can be constructed based on their interaction with laser light. However, a microscopic control over system parameters is difficult to realize in atomic systems. Moreover, finite temperatures and the absence of hardwall system boundaries have limited the observation of topological phenomena.Here, we propose an atom optics-based [23][24][25][26] approach to the study of coherent transport phenomena, which incorporates many of the desired features of atomic and photonic experimental platforms. The scheme we describe is motivated in spirit by magnetic resonance-based * bgadway@illinois.edu techniques for local manipulation via global field addressing [27,28]. In the context of studying transport phenomena, however, we consider an inhomogeneous landscape of site energies, with unique energy differences between neighboring sites, which defines unique tunneling resonances for each site-to-site link. Combined with global field addressing that can drive transitions between neighboring sites, and in particular by simultaneous driving of many such transitions in an amplitude, frequency, and phase-controlled manner, this would allow for local control over the parameters of a discrete lattice model relevant to myriad coherent transport phenomena.Atom optics offers a natural candidate system featuring a quadratic energy lan...

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Edge States and Topological Phases in One-Dimensional Optical Superlattices

Cited by 311 publications

References 38 publications

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Edge state preparation in a one-dimensional lattice by quantum Lyapunov control

Atom-optics approach to studying transport phenomena

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