Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session S24: Topological States in AMO Systems IFocus

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Sponsoring Units: DAMOP DCMP Chair: ChaoXing Liu Room: BCEC 159 
Thursday, March 7, 2019 11:15AM  11:51AM 
S24.00001: Topological triplydegenerate points in ultracold atoms and photonic hyperbolic metamaterials Invited Speaker: Chuanwei Zhang Topological states of matter provide a fertile ground for discovering new quasiparticles in condensed matter physics, such as Weyl and Dirac fermions, which were originally predicted in highenergy physics and recently observed in solidstate materials. In topological semimetals, Weyl and Dirac points correspond to two and fourfold degenerate linear band crossing points, hallmarks of relativistic particles with halfinteger spins. Remarkably, the recent discovery of triply degenerate points (TDPs) in semimetals has opened an avenue for exploring new types of quasiparticles that have no analog in quantum field theory. Such TDPs possess effective integer spins while preserving Fermi statistics and linear dispersions. In previous studies, the emergence of such protected nodes was often attributed to spinvectormomentum couplings. In this talk, I will discuss three new types of TDPs that are classified by different monopole charges (C = +/ 2, 1, 0) and induced by the interplay between spintensor and spinvectormomentum couplings. I will discuss how to realize these new types of TDPs using ultracold atoms in optical lattices and photons in nonHermitian hyperbolic metamaterials. These proposed atomic and photonic systems may provide highly controllable platforms for exploring and engineering novel quasiparticles without counterparts in quantum field theory. 
Thursday, March 7, 2019 11:51AM  12:03PM 
S24.00002: A BoseEinstein Condensate on a Synthetic Hall Cylinder ChuanHsun Li, Yangqian Yan, Sayan Choudhury, David Blasing, Qi Zhou, Yong Chen Interplay between matter and fields in physical spaces with nontrivial geometries gives rise to many exotic quantum phenomena. However, their realizations are often impeded by experimental constraints. Here, we realize a BoseEinstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux, topologically equivalent to a twodimensional (2D) Hall ribbon with two edges connected. This cylindrical surface comprises a real spatial dimension and a curved synthetic dimension formed by cyclicallycoupled spin states. The BEC on such a Hall cylinder has counterintuitive properties unattainable by its counterparts in 2D planes. We observe Bloch oscillations of the BEC with doubled periodicity of the band structure, analogous to traveling on a Möbius strip, reflecting the BEC's emergent crystalline order with nonsymmorphic symmetryprotected band crossings. We further demonstrate such topological operations as gapping the band crossings and unzipping the cylinder. Our work opens the door to engineering synthetic curved spaces and observing intriguing quantum phenomena inherent to the topology of spaces. 
Thursday, March 7, 2019 12:03PM  12:15PM 
S24.00003: Topological Phases of Fermions in Kagome Optical Lattices Vito Scarola, Mengsu Chen, HoiYin Hui, Sumanta Tewari Frustration can favor topological states of matter over conventionally ordered states. We use numerical diagonalization and mean field theory to study models of fermionic atoms and molecules placed in kagome optical lattices. We show that just the long range part of dipolar interactions between fermions can drive the creation of a topological Mott insulator. We also study applications of applied synthetic fields using optical flux lattices and laser assisted tunneling. We find that effective magnetic fields lead to topological phases, including the chiral spin liquid, even for atoms interacting with only the contact interaction. Experimental challenges for realizing these topological states with atomic gases in optical lattices are discussed. 
Thursday, March 7, 2019 12:15PM  12:27PM 
S24.00004: Tomography of Floquet topological singularities: How to measure topological invariants in periodically driven systems Nur Unal, Babak Seradjeh, Andre Eckardt We propose a realistic scheme for the full characterization of Floquet topological insulators realized in optical lattices. We construct a family of drives that connects the target Hamiltonian to a topologically trivial reference point for the periodically driven systems that we identify as the highfrequency regime. Our proposal relies on the detection of topological singularities in the Floquet spectrum with respect to the reference point as the drive parameters are varied within a specific drive family. Bypassing the difficulties of adiabatic preparation through a topological transition, we show how the topological charge of individual singularities can be measured using state tomography techniques. We demonstrate our scheme by using two concrete examples of periodically driven systems in two dimensions relevant to experiments. Our proposal paves the way to full experimental characterization of nonequilibrium topological phases in driven systems with the measurement of both regular and anomalous Floquet topological invariants. 
Thursday, March 7, 2019 12:27PM  12:39PM 
S24.00005: Instantons Emerging from Quench Dynamics of Onedimensional Systems TinLun Ho, Cheng Li “Instantons" were first proposed in high energy physics as a topological solution of YangMills equations in spacetime. We borrow the concept of “instanton" to describe the topological structure in spacetime, constructed from the quench dynamics in ultracold atom systems. In the talk, we shall address the relation between the instantons and the quench dynamics which is determined by 
Thursday, March 7, 2019 12:39PM  12:51PM 
S24.00006: Robustness of Floquet Topology to Temporal Noise Christopher Timms, Rongchun Ge, Michael Kolodrubetz Previous studies on two dimensional periodically driven Floquet systems have demonstrated a novel topological phase known as the anomalous Floquet insulator (AFI). The AFI has quantized, nonadiabatic charge pumping, carried by the chiral edge states of the system. Unlike a Chern insulator, the AFI is able to be localized in the bulk, and this topological response is robust to adding spatial disorder. We consider a more disruptive perturbation, adding temporal noise to each of the Floquet cycles to break the time periodicity. We solve this system numerically in a cylindrical geometry starting from a halffilled state and calculating the net charge pumped around the cylinder during each Floquet period. Surprisingly, we see that the quantization remains for a finite window of temporal disorder up to a time that increases as a power law in system size. We connect the eventual loss of quantization to diffusion of the charge front, which eventually depopulates the topological edge state. This work provides an important insight to how topological Floquet phases might behave in real materials, where noise from the bath is inevitable. 
Thursday, March 7, 2019 12:51PM  1:03PM 
S24.00007: Dynamical quantum phase transitions in U(1) quantum link models YiPing Huang, Debasish Banerjee, Markus Heyl Quantum link models are extensions of Wilsontype lattice gauge theories which realize exact gauge invariance with finitedimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge theories, but also host new phenomena such as crystalline confined phases. We study the nonequilibrium quench dynamics for two representative cases, U(1)quantum link models in (1+1)d and (2+1)d, through the lens of dynamical quantum phase transitions. Finally, we discuss the connection to the highenergy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms. 
Thursday, March 7, 2019 1:03PM  1:15PM 
S24.00008: Quench dynamics for a twodimensional twoband model starting with a topological initial state Xin Chen, Ce Wang, Jinlong Yu We discuss the dynamical process of a twodimensional twoband system starting with a topologically nontrivial initial state, with a nonzero Chern number c_{i}, evolved by a postquench Hamiltonian with Chern number c_{f}. In contrast to the process with c_{i}=0 studied in previous works, this process cannot be classified by the Hopf invariant that is described by the homotopy group π_{3}(S^{2})=Z. It is possible, however, to calculate the ChernSimons integral with a complementary part to cancel the Chern number of initial spin configuration. We show the ChernSimons integral with the complementary part is the topological invariant of this process, which is a linking invariant in the Z_{2c}_{i} class: ν = (c_{f}  c_{i}) mod (2c_{i}). We give concrete examples to illustrate this result and also show the detailed deduction to get this linking invariant. 
Thursday, March 7, 2019 1:15PM  1:27PM 
S24.00009: 1D LocalizationDelocalization Physics and Toroidal Representations of Transfer Matrices Karmela Padavic, Suraj Hegde, Smitha Vishveshwara Wavefunction localization is a characteristic phenomenon occurring in disordered and quasiperiodic systems as well as with edges states in topological phases. We study the quasiperiodic AubryAndreHarper (AAH) model, known to exhibit a unique localizationdelocalization transition in one dimensions, defying standard Anderson localization. Generalizations of the AAH model include nextnearest neighbor (NNN) hopping, or additional incommensurate onsite terms and have so far been studied numerically. For such extended models the appearance of a mobility edge i.e. an energy cutoff dictating which wavefunctions undergo the localizationdelocalization transition is expected. To study properties of these models, we employ transfer matrices which are known to characterize localization physics through Lyapunov exponents. We use the symplectic nature of transfer matrices to represent them as points on a torus. Related wavefunctions then form toroidal curves. We obtain distinct toroidal curves for localized, delocalized and critical wavefunctions, thus demonstrating a geometrical characterization of localization physics. Applying the transfer matrix method to the NNN AAH model, we formulate a geometrical picture that captures the emergence of the mobility edge in a visually striking way. 
Thursday, March 7, 2019 1:27PM  1:39PM 
S24.00010: Topological Marker Currents in Chern Insulators Marcello Davide Caio, Gunnar Möller, Nigel R Cooper, Joe Bhaseen Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment. 
Thursday, March 7, 2019 1:39PM  1:51PM 
S24.00011: Anyon fusion spaces with polar molecules Jacob Covey, Victor Albert, David Aasen, Jason Alicea, Manuel Endres We derive an infinite family of equivalences between fusiontree Hilbert spaces of certain su(2) levelk anyons and atomic ladders constrained by an excitation blockade. The level3 case reduces to the wellknown equivalence between the Hilbert space of a blockaded atomic chain and fusion trees of Fibonacci anyons [1]. These equivalences provide physical realizations of anyonic Hilbert spaces, on top of which one can construct anyonic Hamiltonians and height models. We show how to simulate the level4 chain using ultracold polar molecules in optical lattices by employing two novel capabilities of molecules which are not widely appreciated. Our work paves the way for new directions with ultracold polar molecules that are highly relevant in burgeoning experimental efforts [2]. 
Thursday, March 7, 2019 1:51PM  2:03PM 
S24.00012: Geometric phases enable realworld models of classical and quantum dynamics in Hall effects and in threebody molecular dynamics F. J. Lin Almost sixty years ago, Aharonov and Bohm pointed out that electrons could be affected by vector potentials without an external magnetic field. They described an ad hoc phase shift required for wave functions in vector potentials, e.g., representing magnetic fields. The phase shift exemplifies a geometric phase (or Berry’s phase). In classical and quantum dynamics, vector potentials producing coupled overall rotation lead to geometric phases. Instead of neglecting it, now the coupling is used to create a frame with decoupled overall rotation and vanishing classical and quantum geometric phases. A general formulation of classical dynamics describes both the dynamics of topological matter, such as Hall effects, and threebody molecular dynamics. A quantum extension describes the quantum dynamics of topological matter and the threebody molecular dynamics in the BornOppenheimer approximation. Realworld models with or without magnetic fields contribute to developing optoelectronic and photonic devices. Realworld models for threebody dynamics contribute to developing optimal molecular reaction dynamics. 
Thursday, March 7, 2019 2:03PM  2:15PM 
S24.00013: Topological phases in 1D bosonic Bogoliubov bands with dynamical instability Terumichi Ohashi, Shingo Kobayashi, Yuki Kawaguchi Topological phases of matter have attracted much attention in solidstate physics, but most of studies treat Hermitian Hamiltonians [1]. Recently, there has been growing interest in nonHermitian topological phases [2], which exhibit exotic phenomena absent in Hermitian ones [3]. NonHermitian Hamiltonian describes an open quantum system in which loss and gain of particles coexist. Here, we note that bosonic Bogoliubov quasiparticles, which are elementary excitations from a BoseEinstein condensate (BEC), are also described with a nonHermitian Hamiltonian, where a BEC works as a particle bath. In this sense, topological classification of BECs is an open question. In the case when the nonHermitian Hamiltonian has real eigenvalues, the topological properties of quasiparticles is discussed [4]. 
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