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arXiv:1807.08096 · Physical Review A

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

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

Published Feb 11, 2019• 42 citations
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Abstract

We show that bosonic atoms loaded into orbital angular momentum $l=1$ states of a lattice in a diamond-chain geometry provide a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states that persist across the gap-closing points, indicating the absence of a topological transition. We discuss how to perform the topological characterization of the model with a generalization of the Zak's phase and we show that this system constitutes a realization of a square-root topological insulator. Furthermore, the relative phases arising naturally in the tunneling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realized and observed in ongoing experiments.

DOI
10.1103/physreva.99.023613

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We show that bosonic atoms loaded into orbital angular momentum l=1l=1l=1 states of a lattice in a diamond-chain geometry provide a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states that persist across the gap-closing points, indicating the absence of a topological transition. We discuss how to perform the topological characterization of the model with a generalization of the Zak's phase and we show that this system constitutes a realization of a square-root topological insulator. Furthermore, the relative phases arising naturally in the tunneling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realized and observed in ongoing experiments.
We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of l=1l=1l=1 orbital angular momentum (OAM) states of an optical lattice with a diamond-chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net $\ensuremath{\pi}$ flux through the plaquettes. These effects give rise to a topologically nontrivial band structure and protected edge states which persist everywhere in the parameter space of the model, indicating the absence of a topological transition. By taking advantage of these analytical mappings, we also show that this system constitutes a realization of a square-root topological insulator. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.
We study interaction-induced bound states in a system of ultracold bosons loaded into the states with orbital angular momentum in a one-dimensional staggered lattice of rings. We consider the hard-core limit and strong nearest-neighbour interactions such that two particles in next neighbouring sites are bound. Focusing on the manifold of such bound states, we have derived the corresponding effective model for doublons. With orbital angular momentum l=1l=1l=1, the original physical system is described as a Creutz ladder by using the circulations as a synthetic dimension, and the effective model obtained consists of two Su-Schrieffer-Heeger (SSH) chains and two Bose-Hubbard chains. Therefore, the system can exhibit topologically protected edge states. In a structure that alternates l=1l=1l=1 and l=0l=0l=0 states, the original system can be mapped to a diamond chain. In this case, the effective doublon model corresponds to a Creutz ladder with extra vertical hoppings between legs and can be mapped to two SSH chains if all the couplings in the original system are equal. Tuning spatially the amplitude of the couplings destroys the inversion symmetry of these SSH chains, but enables the appearance of multiple flat bands.
We study a system of a few ultracold bosons loaded into states with orbital angular momentum l=1l=1l=1 of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers +l+l+l and $\ensuremath{-}l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\ensuremath{\phi}$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\ensuremath{\pi}$ flux through the plaquettes. We find nontrivial topological band structures and many-body Aharonov-Bohm caging in the NNN-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\ensuremath{\phi}$ is introduced at an arbitrary lattice periodicity $\mathrm{\ensuremath{\Gamma}}$. For $\mathrm{\ensuremath{\Gamma}}>2$, the $\ensuremath{\pi}$ flux becomes nonuniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.
We show that pairing in an ultracold Fermi gas under spin-orbital-angular-momentum coupling (SOAMC) can acquire topological characters encoded in the quantized angular degrees of freedom. The resulting topological superfluid is the angular analog of its counterpart in a one-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zak phase defined in the angular-momentum space. Upon tuning the SOAMC parameters, a topological phase transition occurs, which is accompanied by the closing of the quasiparticle excitation gap. Remarkably, a topological vortex state can also be stabilized by deforming the Fermi surface, which is topologically nontrivial in both the coordinate and angular-momentum space, offering interesting potentials for applications in quantum information and quantum control. We discuss how the topological phase transition and the exotic vortex state can be detected experimentally.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.