Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum

Pelegrí, G.; Marques, A. M.; Dias, R. G.; Daley, Andrew J.; Mompart, J.; Ahufinger, V.

doi:10.1103/physreva.99.023613

Cited by 41 publications

(40 citation statements)

References 68 publications

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“…In recent years there have been several realizations of flat bands models using optical lattices [73][74][75][76] and more recently the Creutz ladder has been proposed as a workhorse for the study of topological effects in ultracold gases and its implementation seems to be within reach with current experimental tools [43]. The diamond chain has been recently implemented with photonic lattices [77], while excited orbital angular momentum states of ultracold atoms have been proposed as a new venue for implementing the same model [78]. We note also a recent theoretical work [79] where the phase diagram of the diamond chain with a Bose-Hubbard interaction term has been studied in detail and possible strategies for its implementation have been described.…”

Section: Discussionmentioning

confidence: 99%

Preformed pairs in flat Bloch bands

et al. 2018

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In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry in the presence of an attractive Hubbard interaction. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum Φ0/2 = hc/(2e) period, indicating that only bound pairs of particles with charge 2e are propagating, while single quasiparticles with charge e remain localized. For some one dimensional lattice models we show analytically that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover for the same one dimensional lattice models we construct an extensive number of exact conserved quantities. These conserved quantities are associated to the occupation of localized single quasiparticle states and force the single-particle propagator to vanish beyond a finite range. Our results suggest that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.

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Section: Discussionmentioning

confidence: 99%

Preformed pairs in flat Bloch bands

et al. 2018

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“…This automatically implies that the symmetry that protects these states is not usual chiral symmetry associated with bipartite lattices. In fact, one can show that this state is related to the square-root topological insulator [8][9][10][11][12][13] and the protecting symmetry is a sublattice chiral-like hidden symmetry. To our knowledge, topological characterization of a weak topological insulator with compact edge states has not been addressed in the literature where geometrically frustrated lattices are studied [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…In our paper, we show that these compact localized states reflect a different topological transition point (the atomic limit in our case) and consequently they remain completely localized (in the system boundaries, edge or corner) even at the usual transition point t 1 = t 2 where the remaining edge states converge. Our topological characterization follows the approach of [6] which agrees with other methods to address topological invariants that protect finite energy edge states in the case of non-commensurate OBC or non-centered I-axis in the unit cell such as the modified approaches of splitting the Zak's phase into intracell and intercell contributions [17][18][19][20][21], the squaring of the Hamiltonian [8][9][10][11][12][13] and synthetic dimensions [22][23][24][25][26]. The robustness of this compact state is probed when applying a time dependent perturbation to the hopping amplitudes in order to examine its protection against mixing with the bulk states and test the viability of its preparation in a cold atom experiment.…”

Section: Introductionmentioning

confidence: 99%

Enhanced localization and protection of topological edge states due to geometric frustration

et al. 2019

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Topologically non-trivial phases are linked to the appearance of localized modes in the boundaries of an open insulator. On the other hand, the existence of geometric frustration gives rise to degenerate localized bulk states. The interplay of these two phenomena may, in principle, result in an enhanced protection/localization of edge states. In this paper, we study a two-dimensional Lieb-based topological insulator with staggered hopping parameters and diagonal open boundary conditions. This system belongs to the C 2v class and sustains 1D boundary modes except at the topological transition point, where the C 4v symmetry allows for the existence of localized (0D) corner states. Our analysis reveals that, while a large set of boundary states have a common well defined topological phase transition, other edge states reflect a topological non-trivial phase for any finite value of the hopping parameters, are completely localized (compact) due to destructive interference and evolve into corner states when reaching the higher symmetry point. We consider the robustness of these compact edge states with respect to time-dependent perturbations and indicate ways that these states could be prepared and measured in experiments with ultracold atoms.

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“…Specifically, we consider a diamondchain lattice filled with ultracold atoms loaded into orbital angular momentum (OAM) l = 1 states. In this geometry, the OAM degree of freedom induces an effective π flux which yields a single-particle spectrum composed entirely of flat bands upon a proper tuning of the tunneling parameters [45,46]. In this situation, quantum interference leads to a strong localization of noninteracting particles and forbids their propagation through the chain.…”

Section: Introductionmentioning

confidence: 99%

“…In this situation, quantum interference leads to a strong localization of noninteracting particles and forbids their propagation through the chain. This phenomenon, known as Aharonov-Bohm caging [45][46][47][48][49][50], has been recently generalized to non-Abelian systems, where it is expected to yield intriguing state-dependent dynamics [51]. This singleparticle localization effect is a general characteristic of flatband systems [52], wherein the role of the kinetic energy becomes irrelevant and particle motion can only originate from interaction-mediated collective processes.…”

Section: Introductionmentioning

confidence: 99%

Interaction-induced topological properties of two bosons in flat-band systems

Pelegrí

Marques

Ahufinger

et al. 2020

Phys. Rev. Research

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In flat-band systems, destructive interference leads to the localization of noninteracting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighboring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum l = 1 states of a diamond-chain lattice, wherein an effective π flux may yield a completely flat single-particle energy landscape. In the weakly interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

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Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum

Cited by 41 publications

References 68 publications

Preformed pairs in flat Bloch bands

Preformed pairs in flat Bloch bands

Enhanced localization and protection of topological edge states due to geometric frustration

Interaction-induced topological properties of two bosons in flat-band systems

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