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arXiv:1609.02729 · Physical Review A

Single-atom edgelike states via quantum interference

G. Pelegrí, Juan Polo, Alex Turpin, Maciej Lewenstein, J. Mompart, V. Ahufinger

Published Jan 17, 2017• 8 citations
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Abstract

We demonstrate how quantum interference may lead to the appearance of robust edgelike states of a single ultracold atom in a two-dimensional optical ribbon. We show that these states can be engineered within the manifold of either local ground states of the sites forming the ribbon or states carrying one unit of angular momentum. In the former case, we show that the implementation of edgelike states can be extended to other geometries, such as tilted square lattices. In the latter case, we suggest using the winding number associated to the angular momentum as a synthetic dimension.

DOI
10.1103/physreva.95.013614

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We demonstrate how quantum interference may lead to the appearance of robust edgelike states of a single ultracold atom in a two-dimensional optical ribbon. We show that these states can be engineered within the manifold of either local ground states of the sites forming the ribbon or states carrying one unit of angular momentum. In the former case, we show that the implementation of edgelike states can be extended to other geometries, such as tilted square lattices. In the latter case, we suggest using the winding number associated to the angular momentum as a synthetic dimension.
We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two-dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring states with variation of the winding number are complex. In particular, we demonstrate that in a triangular ring configuration the complex nature of the cross-couplings can be used to geometrically engineer spatial dark states to manipulate the transport of orbital angular momentum states via quantum interference.
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.
Abstract A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.
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 propose a cold-atom realization of a zigzag ladder. The two legs of the ladder correspond to a "synthetic" dimension given by two internal (spin) states of the atoms, so that tunneling between them can be realized as a laser-assisted process. The zigzag geometry is achieved by employing a spin-dependent optical lattice with the site position depending on the internal atomic state, i.e., on the ladder's leg. The lattice offers a possibility to tune the single-particle dispersion from a double-well to a single-minimum configuration. In contrast to previously considered semisynthetic lattices with a square geometry, the tunneling in the synthetic dimension is accompanied by spatial displacements of atoms. Therefore, the atom-atom interactions are nonlocal and act along the diagonal (semisynthetic) direction. We investigate the ground-state properties of the system for the case of strongly interacting bosons. In particular, we find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an interesting gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.
We describe a protocol to prepare clusters of ultracold bosonic atoms in strongly interacting states reminiscent of fractional quantum Hall states. Our scheme consists in injecting a controlled amount of angular momentum to an atomic gas using Raman transitions carrying orbital angular momentum. By injecting one unit of angular momentum per atom, one realizes a single-vortex state, which is well described by mean-field theory for large enough particle numbers. We also present schemes to realize fractional quantum Hall states, namely, the bosonic Laughlin and Moore-Read states. We investigate the requirements for adiabatic nucleation of such topological states, in particular comparing linear Landau-Zener ramps and arbitrary ramps obtained from optimized control methods. We also show that this protocol requires excellent control over the isotropic character of the trapping potential.