Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session Y24: Topological States in AMO Systems IIFocus

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Sponsoring Units: DAMOP DCMP Chair: Chuanwei Zhang, University of Texas at Dallas Room: BCEC 159 
Friday, March 8, 2019 11:15AM  11:51AM 
Y24.00001: Higher Order Topological Phases: Quadrupoles, Metamaterials, and Beyond Invited Speaker: Taylor Hughes In this talk we present a new class of phases of matter called higherorder topological phases. Such systems exhibit gapped boundaries that are themselves lowerdimensional topological phases. Furthermore, they manifest topologically protected states at intersections between multiple surfaces. These states can, e.g., carry fractional charge, or be chiral propagating modes. We show that some of the simplest examples of these phases are connected to materials with quantized electric quadrupole moments, and illustrate how they can be realized in a variety of metamaterial systems. We will also review the first experimental evidence for these phases in metamaterial contexts. To characterize these new insulating phases of matter, we introduce a new type of invariant that had been previously overlooked, and we show how these invariants can predict a collection of new phenomena. 
Friday, March 8, 2019 11:51AM  12:03PM 
Y24.00002: Topologically Protected Photonic Modes in Composite Quantum Hall/Quantum Spin Hall Waveguides Shukai Ma, Bo Xiao, Yang Yu, Kueifu Lai, Gennady Shvets, Steven Anlage Photonic topological insulators (PTI) are a new class of structures that can support backscatteringfree propagating waves at an interface between topologically nontrivial structures. In the bianisotropic metawaveguide (BMW) PTI designs, by carefully tuning the geometrical and electromagnetic properties, we can emulate the electronic quantum spin Hall (QSH) effect using its electromagnetic analog. A magnetooptical material added to the structure will introduce a quantum Hall (QH) photonic bulk insulator on the BMW basis. The combined photonic systems with multiple topological phases supporting reflectionfree edgemodes are proposed and experimentally demonstrated. The spin degree of freedom of such topologically protected edgemodes determines their unique pathways through these systems, free from backscattering and able to travel around sharp corners. As an example of their novel properties, we demonstrate a full 4port circulator based on composite QH and QSH backscattering free waveguides. 
Friday, March 8, 2019 12:03PM  12:15PM 
Y24.00003: Interacting Hall Response in Quantum Gas Experiments Sebastian Greschner, Michele Filippone, Thierry Giamarchi Recent experiments with ultracold quantum gases in artificial magnetic fields have shown the possibility to study the Hall effect in quasi onedimensional highly tunable ladder systems. In this context we theoretically analyze the properties of the reactive Hall response on ladder models with strongly interacting bosons and fermions. We compare different methods for the computation of the static Hall coefficient and discuss its dependence on the various methods or limits considered. In the cases relevant for recent experiments in synthetic dimensions, we find a surprising universal behavior of the weak field Hall coefficient of single component phases in the case of an SU(M) symmetric interaction. For strong magnetic fields we study the interesting properties of the quantumHall effect in various quantum phases on ladder geometries including vortexlattice, biased ladder or Laughlin like states. 
Friday, March 8, 2019 12:15PM  12:27PM 
Y24.00004: Higher Order Floquet Topological Insulators with Anomalous Corner States Biao Huang, W.Vincent Liu The theoretical and experimental discovery of topological insulators of higher multipole nature, dubbed “higher order topological insulators” (HOTI), has triggered heated discussions in recent studies. But so far, all researches have been limited to static systems due to the lack of higher order topological invariants constructed for a genuine dynamical system. Here, we report a Floquetdriven model showing the anomalous corner states and a construction of dynamical topological invariant built upon evolution operators $ U(t) $. We show that the bulk static nested quadrupoles, constructed by eigenstates of the static Floquet operator $ U_F = U(T) $, vanish identically, while corner states emerge in all energy gaps with quantized charges due to the dynamical topology. The signature of such an anomalous Floquet phase in cold atom experiments is also discussed via corner particle dynamics and a band tomography. Our work paves the way to the systematic study of HOTI in regimes far away from equilibrium. 
Friday, March 8, 2019 12:27PM  12:39PM 
Y24.00005: Topological states and anomalous localization in nonHermitian systems Víctor M. Martinez Alvarez, Esteban A. RodriguezMena, Luis Foa Torres Recently, the search for topological states has reached to nonHermitian lattices (see [1] and references therein), systems where non Hermiticity models gains and losses (as in photonic crystals) or the effect of interactions (electronelectron, electronphonon). Capital to this endeavor is the ability to build a proper bulkboundary correspondence, a task that has gained much attention during the last year. 
Friday, March 8, 2019 12:39PM  12:51PM 
Y24.00006: NonHermitian adiabatic transport in the space of exceptional points Judith Hoeller, Nicholas Read, Jack Harris An nxn nonHermitian Hamiltonian matrix H can describe a dissipative system, such as n coupled weakly dissipative classical harmonic oscillators. Under full parametric control over H, the parameter space contains a connected  but not simplyconnected  subspace of nth order exceptional points, at each of which H is equivalent to an nxn Jordan block. We show that smooth variations of parameters during time T, along a loop within that space, can single out one state that is least dissipative and evolves adiabatically. Its complex adiabatic phase is T times a Puiseux series in powers of T^{ 1/n}; the coefficient at order T^{0} is the Berry phase, which is a multiple of 2π/n (modulo 2π) and only depends on the homotopy class of the loop within the space of nth order exceptional points. 
Friday, March 8, 2019 12:51PM  1:03PM 
Y24.00007: Topological symmetry classes for nonHermitian models and connections to the bosonic Bogoliubov–de Gennes equation Simon Lieu The BernardLeClair (BL) symmetry classes generalize the AltlandZirnbauer classes in the absence of Hermiticity. Within the BL scheme, timereversal and particlehole symmetry come in two flavors, and “pseudoHermiticity” generalizes Hermiticity. We propose that these symmetries are relevant for the topological classification of nonHermitian singleparticle Hamiltonians and Hermitian bosonic Bogoliubov–de Gennes (BdG) models. We show that the spectrum of any Hermitian bosonic BdG Hamiltonian is found by solving for the eigenvalues of a nonHermitian matrix which belongs to one of the BL classes. We therefore suggest that bosonic BdG Hamiltonians inherit the topological properties of a nonHermitian symmetry class and explore the consequences by studying symmetryprotected edge instabilities in a onedimensional system. 
Friday, March 8, 2019 1:03PM  1:15PM 
Y24.00008: Stability of NonHermitian Phases Dan Borgnia Recent work on nonHermitian physics in condensed matter systems has focused on the classification of new topological phases. The notion of a gap usually used to describe the stability of Hermitian phases is not sufficient in the presence of loss and gain terms. This work uses known results in the theory of psuedospectra and Jordan Normal Forms to detail the stability of novel nonHermitian phases under different disorder profiles in 1D with some generalizations into higher dimensions. We find agreement with previous work in simple chiral models and single parameter disorder distributions of our generalized stability arguments. 
Friday, March 8, 2019 1:15PM  1:27PM 
Y24.00009: Topological charge pumping in the interacting bosonic RiceMele model Andrew Hayward, Christian Schweizer, Michael Lohse, Monika Aidelsburger, Fabian HeidrichMeisner In recent years, demonstrations of topological Thouless charge pumping have been performed with ultracold atoms. We discuss our recent work [1] investigating charge pumping in the Bosonic RiceMele model and verify that the charge pumping remains quantized as long as the pump cycle avoids the superfluid phase. In the limit of hardcore bosons, the quantized pumped charge can be understood from singleparticle properties such as the integrated Berry curvature constructed from Bloch states, while this picture breaks down at finite interaction strengths. These two properties  robust quantized charge transport in an interacting system of bosons and the breakdown of a singleparticle invariant  could both be measured with ultracold quantum gases extending a previous experiment [2]. We also relate the structure of the spectral flow of the entanglement spectrum to the properties of the charge pump. 
Friday, March 8, 2019 1:27PM  1:39PM 
Y24.00010: Topologically robust defect states in twofold $\mathcal{PT}$symmetric systems SangJun Choi, JungWan Ryu, Hee Chul Park The emergence of topologically robust states has been understood in terms of the bulkedge correspondence; they appear at the boundary between two insulating systems whose topology cannot be continuously deformed into another. However, is its converse true? Here, we find that at the boundary where two topologically trivial insulating system meets, a robust localized state can appear. We provide a new topological identification where twofold $\mathcal{PT}$symmetry of the system protects the emergence of such a state against continuous deformations. Moreover, we show the localization length of the topological defect state is insensitive to a wide range of parameters, and the defect states in the known systems fall into our topological identification. 
Friday, March 8, 2019 1:39PM  1:51PM 
Y24.00011: Topological insulators in synthetic dimensions David Long, Philip Crowley, Ivar Martin, Anushya Chandran Few level quantum systems driven by multiple incommensurate external tones exhibit temporal analogs of many realspace topological phenomena. I will discuss how a qubit driven by two tones realizes a topological insulator in frequency space and identify the symmetry protecting the insulator. The edge modes of the topological insulator can robustly transfer a large amount of energy between the drives for symmetrybroken initial states. 
Friday, March 8, 2019 1:51PM  2:03PM 
Y24.00012: Interactioninduced multivaluedness and topological change between quantum current and its variance ChihChun Chien, Mekena Metcalf, ChenYen Lai, Massimiliano Di Ventra The variance of a quantum observable has been an important quantity in quantum mechanics, and it can reveal additional information beyond the average. By analyzing the parametric curves of the quantum current versus its variance, we found a general change of topology due to the interactions . We consider a benzenelike lattice with fermions driven by a magnetic flux for the isolated system and a threesite lattice connected driven by two particle reservoirs for the open system. In both systems, there is a onetoone correspondence between the current and its variance in absence of interactions. When the interactions are introduced, the parametric curves exhibit loop structures and show multivalued correspondence between the current and its variance. The phenomena could be realizable using available coldatom technology. 
Friday, March 8, 2019 2:03PM  2:15PM 
Y24.00013: Orderfromdisorder effects and Zeeman field tuned quantum phase transitions in a bosonic quantum anomalous Hall system Fadi Sun, Jinwu Ye We study possible many body phenomena in the recent experimentally realized weakly interacting quantum anomalous Hall system of spinor bosons by Wu, et.al, Science 354, 8388 (2016). At a zero Zeeman field h = 0, by incorporating order from disorder effects, we determine the quantum ground state to be a N = 2 XYantiferromagnetic superfluid state and also evaluate its excitation spectra. At a finite small h, the competition between the Zeeman energy and the effective potential generated by the orderfromdisorder leads to a canted antiferromagnetic superfluid state, then drives a second order transition to a spinpolarized superfluid state along the z direction. The transition is in the same universality class as the zero density superfluid to Mott transition. Scaling behaviours of various physical quantities are derived. The ongoing experimental efforts to detect these novel phenomena are discussed. 
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