Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session K13: Topological States in AMO SystemsFocus

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Sponsoring Units: DAMOP Chair: Norman Yao, University of California, Berkekely Room: 272 
Wednesday, March 15, 2017 8:00AM  8:36AM 
K13.00001: Abstract Withdrawn Invited Speaker: Topological properties lie at the heart of many fascinating phenomena in solidstate systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentumresolved state tomography from which we obtain the Berry curvature and Chern number (Science 352, 1091 (2016)). \newline \newline Furthermore, we study the timeevolution of the manybody wavefunction after a sudden quench of the lattce parameters and observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at critical times. Our measurements constitute the first observation of a so called \quotedsinglbase dynamical topological phase transition`, which we show to be a fruitful concept for the understanding of quantum dynamics far from equilibrium (arXiv 1608.05616). 
Wednesday, March 15, 2017 8:36AM  8:48AM 
K13.00002: Topologically protected dynamical quantum phase transitions Zhoushen Huang, Alexander Balatsky A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e. the Loschmidt echo—vanishes at critical times $\{t^*\}$. Analytical results to date are limited to twoband models, leaving the exact relation between topology and DQPT unclear. In this work, we show that for a general multiband system, a robust DQPT relies on the existence of nodes (i.e. zeros) in the wavefunction overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wavefunctions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a threeband generalized Hofstadter model. We also discuss possible experimental observations. [Preview Abstract] 
Wednesday, March 15, 2017 8:48AM  9:00AM 
K13.00003: Floquet topological insulator in an optical lattice with modulated lattice depth Yangqian Yan, Tony Lee We propose a simple scheme to realize a Floquet topological insulator in an optical lattice by weakly modulating the lattice depth. When the modulation frequency resonantly couples the s and p bands, the Floquet Hamiltonian becomes topologically nontrivial. We map out the topological transition as a function of frequency and amplitude. We also confirm the bulk topology by finding edge states in a lattice with open boundary conditions. An advantage of our scheme is that the modulation amplitude can be relatively small, so the heating can be minimal. [Preview Abstract] 
Wednesday, March 15, 2017 9:00AM  9:12AM 
K13.00004: Selfsimilarity in Floquet topological insulators at low frequencies Martin RodriguezVega, Babak Seradjeh We study theoretically the lowfrequency regime of Floquet topological insulators. Specifically, we consider a periodicallydriven onedimensional SuSchriefferHeeger (SSH) model, for which we calculate, analytically and numerically, the quasienergy spectrum. We study the behavior of the quasienergy gap as a function of drive frequency and other parameters and find selfsimilar spectral patterns. We also study the topological phase transitions, finding that they are present for arbitrarily small frequencies. We obtain the topological invariants as a function of the system's parameters, and compare with the explicit calculation of localized edge states for systems with open boundary conditions. Finally, we discuss the relevance of our results for the understanding of the longtime adiabatic limit in Floquet systems. [Preview Abstract] 
Wednesday, March 15, 2017 9:12AM  9:24AM 
K13.00005: Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator Hossein Dehghani, Aditi Mitra Results are presented for the occupation probabilities and current densities of bulk and edge states of halffilled graphene in a cylindrical geometry, and irradiated by a circularly polarized laser. It is assumed that the system is closed, and that the laser has been switched on as a quench. Laser parameters corresponding to some representative topological phases are studied: one where the Chern number of the Floquet bands equals the number of chiral edge modes, a second where anomalous edge states appear in the Floquet Brillouin zone boundaries, and a third where the Chern number is zero, yet topological edge states appear at the center and boundaries of the Floquet Brillouin zone. Qualitative differences are found for the high frequency offresonant and low frequency onresonant laser with edge states arising due to resonant processes occupied with a high effective temperature on the one hand, while edge states arising due to offresonant processes occupied with a low effective temperature on the other. Finally, we study the effects of inversion symmetry and particlehole symmetry on the net current density and occupation probabilities in a halffilled system. [Preview Abstract] 
Wednesday, March 15, 2017 9:24AM  9:36AM 
K13.00006: Symmetryprotected edge states in periodically driven band insulators Oleksandr Balabanov, Henrik Johannesson The symmetryprotected edge states in topologically nontrivial band insulators are robust to any perturbations that are localized on the edges and preserve the relevant symmetries. In recent work we have found that the edge states in driven (Floquet) systems may be resistant to a much broader class of perturbations as compared to the timeindependent case. We illustrate our finding by a numerical computation on the harmonically driven SSH model. A proposal for an experimental test using cold atoms is presented. [Preview Abstract] 
Wednesday, March 15, 2017 9:36AM  9:48AM 
K13.00007: Quantized magnetization density in periodically driven systems Frederik Nathan, Mark Rudner, Netanel Lindner, Erez Berg, Gil Refael We identify a new bulk quantized observable – the magnetization density  that serves as a topological order parameter for periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. While all Floquet states are localized when considered stroboscopically over a full period, the micromotion within the driving period may carry a nontrivial orbital magnetization. We find that the timeaveraged magnetization density when the system is filled with fermions is quantized in units of the inverse driving period. We furthermore show that a quantized current flows around the boundary of any filled region of finite extent. The quantization has a topological origin: we relate the timeaveraged magnetization density to the winding number characterizing the new phase identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding number invariant can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in a system of cold atoms in an optical lattice. [Preview Abstract] 
Wednesday, March 15, 2017 9:48AM  10:00AM 
K13.00008: Driven Phases of Quantum Matter Vedika Khemani, Curt von Keyserlingk, Achilleas Lazarides, Roderich Moessner, Shivaji Sondhi Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial ``infinitetemperature'' Floquetergodic phase.~By contrast, I will show that their disordered Floquet manybody localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting. I will show that a subset of these novel phases are~\textit{absolutely stable~}to all weak local deformations of the underlying Floquet drives, and spontaneously break Hamiltonian dependent~\textit{emergent}~symmetries.~Strikingly, they simultaneously also break the underlying timetranslation symmetry of the Floquet drive and the order parameter exhibits oscillations at multiples of the fundamental period. This ``timecrystallinity'' goes hand in hand with spatial symmetry breaking and, altogether, these phases exhibit a novel form of simultaneous longrange order in space and time. I will describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states. [Preview Abstract] 
Wednesday, March 15, 2017 10:00AM  10:12AM 
K13.00009: Hofstadter's Butterfly in Onedimensional Driven Quantum Systems Pengfei Liang, Michael Marthaler, Lingzhen Guo A novel way to produce Hofstadter's butterfly is proposed in onedimensional driven quantum systems. The system, which is modeled as a periodically kicked harmonic oscillator, creates various lattice structures in phase space. We develop the band theory of the square lattice and show that the Hofstadter's butterfly appears in the fractal quasienergy spectrum as a consequence of both the periodic lattice structure and the noncommutative geometry of phase space. We further introduce the concept pseudospin to distinguish degenerate states. Our proposal opens up the possibility to observe fractal structure in onedimensional quantum systems and may bring a new way for quantum simulation. [Preview Abstract] 
Wednesday, March 15, 2017 10:12AM  10:24AM 
K13.00010: Quadratic band touching points and flat bands in twodimensional topological Floquet systems Liang Du, Xiaoting Zhou, Gregory Fiete In this work we theoretically study, using FloquetBloch theory, the influence of circularly and linearly polarized light on twodimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flatband dispersionless. We find a small gap is also opened at the quadratic band touching point by 2photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective lowenergy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems. [Preview Abstract] 
Wednesday, March 15, 2017 10:24AM  10:36AM 
K13.00011: Topological Bloch oscillations Judith Hoeller, Aris Alexandradinata We propose a new way to characterize topological crystalline insulators without robust surface signatures. A topological insulator in an electric field is characterized by a recurrence time which is an integer multiple of the usual Bloch period. This same integer is a topological invariant protected by crystal symmetries, and divides n for nfold rotationallysymmetric crystals. We explain the origin of topological Bloch oscillations from two dual perspectives: from symmetric parallel transport of Bloch states in the Brillouin zone, and from Wannier functions which are fixed to Wyckoff positions. By considering deformations of energy bands, we estimate how long topological Bloch oscillations survive. [Preview Abstract] 
Wednesday, March 15, 2017 10:36AM  10:48AM 
K13.00012: Protocols for probing topological edge modes and dimerization with atomic fermions in optical potentials Mekena Metcalf, ChenYen Lai, ChihChun Chien We propose protocols to probe localized edge states in a dimerized chain using cold Fermi gases. Standard trapping methods impose a confining harmonic potential preventing detection of edge states because addition of the trapping potential fuses zeroenergy eigenstates into the bulk energy spectrum. An alternative trapping method with atoms confined in ring lattice, whose boundary conditions are transformed from periodic to open using an off resonant laser sheet, will induce topological modes under suitable conditions. Addition of a timedependent artificial gauge field along the circumference of the ring results in mass transport mainly from bulk modes; measurement of the density demonstrates the remaining edge state. Signatures of dimerization in the presence of onsite interactions can be found in correlations as the system transforms from periodic to open boundary conditions. Persistence of finite correlations when the system undergoes a boundary transformation reveals a memory effect of the dimerized, initial structure. [Preview Abstract] 
Wednesday, March 15, 2017 10:48AM  11:00AM 
K13.00013: Measurement Protocol for the Topological Uhlmann Phase 
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