Topological Fractional Pumping with Alkaline-Earth-Like Atoms in Synthetic Lattices

Taddia, Luca; Cornfeld, Eyal; Rossini, Davide; Mazza, Leonardo; Sela, Eran; Fazio, Rosario

doi:10.1103/physrevlett.118.230402

Cited by 86 publications

(69 citation statements)

References 57 publications

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“…In the last few years, a series of remarkable experiments has demonstrated how cold atomic gases in optical lattices can realize topological band structures [1][2][3][4][5][6][7] with a high degree of accuracy and tunability [8][9][10][11][12]. In the context of one-dimensional (1D) systems, ladders pierced by synthetic gauge fields [13][14][15][16][17][18][19][20][21][22][23] have been experimentally shown to display a plethora of phenomena, including chiral currents [24] and edge modes akin to the two-dimensional Hall effect [7], accompanied with the long-predicted-but hard to directly observeskipping orbits [25,26]. While such phenomena have required relatively simple microscopic Hamiltonians apt to describe electrons in a magnetic field [27], the flexibility demonstrated in very recent settings utilizing alkaline-earth-like atoms [28][29][30][31][32][33] has shown how a new class of model Hamiltonians-where nearest neighbor couplings on multi-leg ladders can be engineered almost independently one from the other-is well within experimental reach.…”

Section: Introductionmentioning

confidence: 99%

Topological Devil’s staircase in atomic two-leg ladders

et al. 2019

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We show that a hierarchy of topological phases in one dimension-a topological Devil's staircasecan emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.

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Section: Introductionmentioning

confidence: 99%

Topological Devil’s staircase in atomic two-leg ladders

et al. 2019

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“…Recent proposals have been put forth for cylindrical geometries [30,31]. A recent experiment demonstrates both a synthetic magnetic field for the photons hopping in a three-qubit loop with periodically modulated couplers and repulsive interactions mediated by the qubits [32], which forms a scalable platform for fractional quantum Hall states of bosons.…”

Section: Introductionmentioning

confidence: 99%

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

et al. 2017

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We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at ν = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

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“…In this work, we have neglected the role of atom-atom interactions which are expected to drive synthetic ladders pierced by a synthetic magnetic flux into exotic phases connected with the fractional quantum Hall physics [30][31][32][33][34][35]. Motivated by these previous findings, we leave as an intriguing perspective a characterization of the topological phases discussed in this paper in the presence of interactions and the search for other interacting topological phases at lower fillings.…”

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confidence: 99%

Topological phases in frustrated synthetic ladders with an odd number of legs

et al. 2018

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The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry, and is protected by a properly defined inversion symmetry. We start our analysis considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum and a non-zero Zak phase; then, we generalize our findings -addressable in the state-of-the-art cold atom experiments -to ladders with an higher number of legs. The Hofstadter problem [1] describing a particle hopping on a two-dimensional lattice pierced by a magnetic field, is a paradigm of quantum mechanics. Formulated more then forty years ago, it embeds a multitude of seminal notions in modern condensed matter physics [2]: topological bands, edge excitations, fractal properties of the spectrum, just to mention some of them. Despite its apparent simplicity and the enormous body of investigation both theoretical and experimental [3][4][5][6][7], the Hofstadter problem still hides some surprises, as we are going to discuss in the following.The motivation of our work stems from the recent realization [8-10] of the Hofstadter Hamiltonian in optical lattices with a synthetic dimension. The possibility of engineering an additional (synthetic) few sites long dimension [11,12] with non-trivial boundary conditions by using some internal degrees of freedom of the atoms has encouraged the study of the Hofstadter Hamiltonian in a strongly anisotropic geometry [13].(a) Is this a new territory for the Hofstadter problem or are we bound to detect a smooth crossover from a two-to a one-dimensional behavior? A naïve expectation would induce to think that synthetic lattices can simulate a two-dimensional geometry when the transverse dimension is much longer than the correlation length of the system along the transverse dimension itself, and they turn out to be effectively one-dimensional when the number of sites in the transverse direction is small, such as in synthetic ladders. In this work, we show that in the presence of a selected applied magnetic field and for an odd number of legs (L y ), this simple picture fails and the Hofstadter Hamiltonian can host unexpected topological phases for suitable values of the flux piercing the ladder. These phases, addressable in the state-of-the-art cold-atom experiments [8,9], are protected by a hidden inversion symmetry and exhibit the typical features of topological states in one dimension, i.e., exponentially localized degenerate edge states, a non-zero Zak phase [14][15][16], and a degenerate entanglement spectrum [17,18]. Note, however, that they...

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Topological Fractional Pumping with Alkaline-Earth-Like Atoms in Synthetic Lattices

Cited by 86 publications

References 57 publications

Topological Devil’s staircase in atomic two-leg ladders

Topological Devil’s staircase in atomic two-leg ladders

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Topological phases in frustrated synthetic ladders with an odd number of legs

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