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arXiv:1703.03735 · Europhysics Letters (EPL)

Protocols for dynamically probing topological edge states and dimerization with fermionic atoms in optical potentials

Mekena Metcalf, Chen-Yen Lai, Kevin Wright, Chih-Chun Chien

Published Jun 1, 2017• 7 citations
arXivHTMLPDF

Abstract

Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold atoms hinder the direct detection of topological edge states arising at the boundary because the distortion fuses the edge states into the bulk. We propose experimentally feasible protocols to probe localized edge states and dimerization of ultracold fermions. By confining cold atoms in a ring lattice and changing the boundary condition from periodic to open using an off-resonant laser sheet to cut open the ring, topological edge states can be generated. A lattice in a topological configuration can trap a single particle released at the edge as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals the occupied edge states. Signatures of dimerization in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state distinguishing different configurations.

DOI
10.1209/0295-5075/118/56004

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Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold atoms hinder the direct detection of topological edge states arising at the boundary because the distortion fuses the edge states into the bulk. We propose experimentally feasible protocols to probe localized edge states and dimerization of ultracold fermions. By confining cold atoms in a ring lattice and changing the boundary condition from periodic to open using an off-resonant laser sheet to cut open the ring, topological edge states can be generated. A lattice in a topological configuration can trap a single particle released at the edge as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals the occupied edge states. Signatures of dimerization in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state distinguishing different configurations.
Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.
Conventional topological insulators exhibit exotic gapless edge or surface states, as a result of non-trivial bulk topological properties. In periodically-driven systems the bulk-boundary correspondence is fundamentally modified and knowledge about conventional bulk topological invariants is insufficient. While ultracold atoms provide excellent settings for clean realizations of Floquet protocols, the observation of real-space edge modes has so far remained elusive. Here we demonstrate an experimental protocol for realizing chiral edge modes in optical lattices, by creating a topological interface using a potential step that is generated with a programmable optical potential. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes that are realized in a periodically-driven honeycomb lattice. Controlling the height and sharpness of the potential step, we study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.
We propose the realization of topological quantum states in a cold-atom system, using a two-dimensional hexagonal optical lattice and a light-induced periodic vector potential. A necessary condition for observing the topological states is the realization of a confining potential with a flat bottom and sharp boundaries. To probe the topological states, we propose to load bosons into the characteristic edge states and image them directly. The possibility of mapping out the edge states and controlling the optical lattice and vector potentials offers opportunities for exploring topological phases with no equivalent in condensed-matter systems.
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes - guaranteed by the existence of non-trivial topological invariants - have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas, and imaging its time-evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes--guaranteed by the existence of nontrivial topological invariants--have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.