Schedule for: 17w5144 - Photonic Topological Insulators

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In this talk I will review some general aspects about the different ways of injecting light into a topological photonics system and of extracting information about its dynamics from the emitted light. Rather than just a hindrance, the intrinsically non-equilibrium nature of optical systems can in fact be seen as a promising asset in view of exploring new physics beyond what is normally done in condensed-matter and ultracold atom systems. In the first part, I will review the basic features of the principal pumping schemes used in experi- ments on quantum fluids of light [1] and topological photonics. In particular, I will illustrate how these features have been exploited in recent experiments to highlight different aspects of topological physics. In the second part, I will present some theoretical proposals of new effects that can be studied in state-of-the-art systems of current interest for topological photonics. Our long term goal is to push further the research on topological photonics in the direction of generating strongly correlated states of light in strongly nonlinear systems [2, 3] and observe novel phase transitions in a driven-dissipative context [4]. References [1] I. Carusotto and C. Ciuri, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013) [2] E. Macaluso and I. Carusotto, Hard-wall confinement of a fractional quantum Hall liquid, arXiv:1706.00353. [3] R. O. Umucallar and I. Carusotto, Spectroscopic signatures of a Laughlin state in an incoher- ently pumped cavity, to be submitted. [4] J.Lebreuillyetal.,Stabilizingstronglycorrelatedphotonfluidswithnon-Markovianreservoirs, arXiv:1704.01106.

Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most notably, local geometrical characteristics, like the Berry curvature, can be related to global topological invariants such as those classifying quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the dynamical evolution of a wave-packet [1]. We experimentally demonstrate for the first time that wave-packet dynamics can be used to directly map out the Berry curvature over an energy band [2]. To this end, we use optical pulses in two coupled fibre loops to explore the discrete time-evolution of a wave-packet in a 1D geometrical charge pump, where the Berry curvature leads to an anomalous displacement of the wave packet under pumping. This is a direct observation of Berry curvature effects in an optical system, and, more generally, a proof-of-principle demonstration that wave-packet dynamics can be used as a high-resolution tool for probing the geometrical properties of energy bands. [1] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010). [2] M. Wimmer, H.M. Price, I. Carusotto and U. Peschel, Nature Physics, 13, 6, 545 (2017).

I discuss recent developments of the study of “synthetic dimensions” in photonics. The idea of synthetic dimensions is to identify internal states of a photonic cavity as extra dimensions, and to simulate higher dimensional lattice models using physically lower dimensional systems. The concept was originally proposed and experimentally realized in ultracold gases [1–5]. I first review the existing theoretical and experimental studies of synthetic dimensions. After discussing some challenges and limitations of the existing methods of synthetic dimensions, I explain our proposals of realizing synthetic dimensions in photonic cavities [6, 7], which overcome some of these limitations. Finally I discuss how the four dimensional quantum Hall effect can be observed in photonics using the synthetic dimensions [6, 8, 9]. [1] O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, Quantum Simulation of an Extra Dimension, Phys. Rev. Lett. 108, 133001 (2012). [2] A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzelinas, and M. Lewenstein, Synthetic Gauge Fields in Synthetic Dimensions, Phys. Rev. Lett. 112, 043001 (2014). [3] M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science 349, 1510 (2015). [4] B. K. Stuhl, H. I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science 349, 1514 (2015). [5] L. F. Livi, G. Cappellini, M. Diem, L. Franchi, C. Clivati, M. Frittelli, F. Levi, D. Calonico, J. Catani, M. Inguscio, and L. Fallani, Synthetic dimensions and spin-orbit coupling with an optical clock transition, Phys. Rev. Lett. 117, 220401 (2016). [6] T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics Phys. Rev. A 93, 043827 (2016). [7] T. Ozawa and I. Carusotto, Synthetic dimensions with magnetic fields and local interactions in pho- tonic lattices, Phys. Rev. Lett. 118, 013601 (2017). [8] H. M. Price, O. Zilberberg, T. Ozawa, I. Carusotto, and N. Goldman, Four-Dimensional Quantum Hall Effect with Ultracold Atoms, Phys. Rev. Lett. 115, 195303 (2015). [9] H.M.Price,O.Zilberberg,T.Ozawa,I.Carusotto,andN.Goldman,MeasurementofChernnumbers through center-of-mass responses, Phys. Rev. B 93, 245113 (2016).

The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. A prominent example thereof is the two-dimensional integer quantum Hall effect. It is characterized by the first Chern number which manifests in the quantized Hall response induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional systems leads to the appearance of a novel non-linear Hall response with a 4D symmetry that is quantized as well, but described by a 4D topological invariant - the second Chern number. Here, we report on the first realization of such 4D topological effects using 2D topological pumps. The quantized bulk response of the pump is measured in a cold atomic system and its corresponding edge phenomena is studied using coupled photonic waveguide arrays.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

We describe topological crystalline insulators in 2D that host corner-localized modes. These insulators are protected by spatial group symmetries, and hence do not need time-reversal symmetry to be broken. As initially described in Science 357, 61 (2017), the bulk-boundary correspondence in these systems allows for the edges of the 2D crystal to be gapped, as long as the edges are 1D topological insulators themselves. We will show the experimental realization of one such structure in a photonic system. We also describe topological pumping processes associated with these insulators that are higher dimensional counterparts of the Thouless charge pump. When these pumping processes are extended into 3D via reverse dimensional reduction procedures, the systems break time-reversal symmetry and give rise to chiral, hinge-localized modes.

In the first part of the talk, I discuss how optical nonlinearity alters the behavior of photonic topological insulators. In the nonlinear regime, band structures and their associated topological invariants cannot be calculated. Nonetheless, nonlinear photonic lattices can support moving edge solitons that "inherit" many properties of linear topological edge states: they are strongly self-localized, and propagate unidirectionally along the lattice edge. These solitons can be realized in a variety of model systems, including (i) an abstract nonlinear Haldane model, (ii) a Floquet lattice of coupled helical waveguides, and (iii) a lattice of coupled-ring waveguides. Topological solitons can be "self-induced", meaning that they locally drive the lattice from a topologically trivial to nontrivial phase, similar to how an ordinary soliton locally induces its own confining potential. This behavior can be used to design nonlinear photonic structures with power thresholds and discontinuities in their transmittance; such structures, in turn, may provide a novel route to devising nonlinear optical isolators. In the second part of the talk, I discuss amorphous analogues of a two-dimensional photonic Chern insulator. These lattices consist of gyromagnetic rods that break time-reversal symmetry, arranged using a close-packing algorithm in which the level of short-range order can be freely adjusted. Simulation results reveal strongly-enhanced nonreciprocal edge transmission, consistent with the behavior of topological edge states. Interestingly, this phenomenon persists even into the regime where the disorder is sufficiently strong that there is no discernable spectral gap.

Recently, the exploration of topological physics in photonic structures has triggered considerable efforts to engineer optical devices that are robust against external perturbation and fabrication defects [1]. However, due to the difficulty of implementing topological lattices in media exhibiting optical gain and/or nonlinearities, these realizations have been mostly limited so far to passive devices. Hence, cavity polaritons formed from the strong coupling between quantum well excitons and cavity photons are particularly appealing: their photonic part allows for engineering topological properties in lattices of coupled resonators [2,3], while their excitonic part gives rise to Kerr-like nonlinearities and to lasing through stimulated relaxation [4]. In this work [5], we demonstrate lasing in the topological edge states of a 1D lattice. This lattice emulates an orbital version of the Su-Schrieffer-Heeger (SSH) Hamiltonian by coupling the 1st excited states (l=1) of polariton micropillars arranged in a zigzag chain (Fig 1 shows a SEM image of the lattice and a schematic representation of a micropillar, and Fig. 2 shows a real-space image of the emission from the orbital bands where we can observe the spatial distribution of the topological mode). Then, taking profit of the nonlinear properties of polaritons, we evaluate the robustness of this lasing action by optically shifting the on-site energy of the edge pillar, thus breaking the chiral symmetry of the lattice. Under this perturbation, we observe that the localization of the topological mode is not significantly affected, leading to an immunity of the lasing threshold. The most promising perspective of this work is to extend the results to 2D lattices where we envision, in systems with broken time-reversal symmetry, topological lasers in 1D chiral edge states allowing backscattering-immune transport of coherent light. References [1] L. Lu., J. Joannopoulos, and M. Soljacic. Nat. Photon. 8, 821 (2014) [2] M. Milicevic et al. Phys. Rev. Lett 118, 107403 (2017) [3] F. Baboux et al. Phys. Rev. B 95, 161114 (R) (2017) [4] I. Carusotto and C. Ciuti. Rev. Mod. Phys. 85, 299 (2013) [5] P. St-Jean et al. arXiv: 1704.07310 (accepted for publication in Nat. Photon.)

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

The talk presents rigorous theorems for Schroedinger operators with the symmetries of the honeycomb. The results deal with Dirac points and low-lying bands in the weak binding and strong binding regimes, and in intermediate regimes. Joint work with Michael Weinstein and James Lee-Thorp.

Abstract: We present rigorous results on protected edge states for continuous Schroedinger operators with honeycomb potentials. We consider edges which arise (a) via interpolation, by a domain wall, between two distinct periodic potentials, and (b) at the sharp interface between a honeycomb structure and a homogeneous media. Joint work with Charles Fefferman and James Lee-Thorp.

A systematic method to find tight-binding approximations in longitudinally driven linear/nonlinear photonic lattices is developed; prototypes include honeycomb and staggered square lattices. A number of periodic helically varying lattices are investigated; these include: sublattices with the same rotation, phase offset rotation, counter rotation, different rotation sizes and frequencies. Both topological and nontopological modes are found. Topological modes possess unidirectionality and do not scatter off lattice defects. Asymptotic descriptions are found; numerical simulations for both the linear and nonlinear edge states agree with asymptotic theory.

Motivated by the novel and subtle properties of electronic waves in graphene, there has been very wide interest in the propagation of waves in two-dimensional structures having the symmetries of a hexagonal tiling of the plane with applications to electromagnetic and other types of waves. In this talk, we analyze the photonic analogs of graphene and related topological edge states. Specifically, we study the propagation of waves governed by the two-dimensional Maxwell equations in honeycomb media. Existence of Dirac Ferminons and correspoinding Dirac dynamics are regiously analyzed. The introduction through small and slow variations of a domain wall across a line-defect gives rise to the bifurcation from Dirac points of highly robust (topologically protected) edge states. This talk is based on the joint work with Michael I. Weinstein at Columbia University and James Lee-Thorp at Courant Institute.

We study the dynamics of wave-packets in media with a local periodic structure which varies adiabatically (over many periods of the periodic lattice) across the medium. We focus in particular on the case where symmetries of the periodic structure lead to degeneracies in the Bloch band dispersion surface. An example of such symmetry-induced degeneracies are the `Dirac points’ of media with `honeycomb lattice’ symmetry. Our results are as follows: (1) A systematic and rigorous derivation of the `anomalous velocity’ of wave-packets due to the Bloch band’s Berry curvature. The Berry curvature is large near to degeneracies, where it takes the form of a monopole. We also derive terms which do not appear in the works of Niu et al. (2) Restricting to one spatial dimension, the derivation of the precise dynamics when a wave-packet is incident on a Bloch band degeneracy. In particular we derive the probability of an inter-band transition and show that our result is consistent with an appropriately interpreted Landau-Zener formula. I will present these results for a Schr\”{o}dinger model; extending our results to the full Maxwell system is the subject of ongoing work. This is joint work with Michael Weinstein and Jianfeng Lu.

Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal, or macroscopic constituents. These active liquids can flow spontaneously even in the absence of an external drive. Unlike spontaneous active flow, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials.

In this talk, I will review our recent progress towards the concept, design and realization of magnet-free non-reciprocal photonic, acoustic and mechanical devices, and arrays of them offering strong topological protection, aimed at realizing reconfigurable, broadband isolators, gyrators and circulators, and one-way waveguides. We will discuss our approaches to induce topological order, and to design topological photonic metasurfaces based on spatio-temporal modulation, nonlinearities, and/or opto-mechanical interactions, and discuss our vision towards new transport phenomena for light and sound, and new nanophotonic and acoustic devices with enhanced non-reciprocal properties over broad bandwidths.

All existing topological band structures can be traced back to a quantized dipole moment, or a mathematical generalization thereof. Recently, it has been shown theoretically, how the quadrupole moment of a charge distribution can be quantized. The associated phenomenology includes in-gap states on surfaces two or more dimensions lower than the bulk. Here, we report on the experimental observation of such a quadrupole state in a mechanical metamaterial made from weakly coupled oscillators in a silicon membrane. We characterize the topological in-gap “corner-states” together with the induced gapped edge modes.

Radiation pressure of electromagnetic fields have been widely used for non-contact nanomanipulation and tunable optics. However, for the resulting force fields, the backscattering of light has been a major constraint that result in instability and dissipation. Here we show that the complete suppression of backscattering in photonic topological materials provides new ways of controlling optical forces: long range optical pulling forces exist in any line defect containing multiple edge states, while long range conservative potentials can be established with single-mode edge states. The optical force fields are entirely defined by the topological band structures and the unit cell functions.

Geometry, topology and broken symmetry often play a powerful role in determining the organization and properties of materials. A recent example is the discovery that the excitation spectra of materials -- be they electronic, optical, or mechanical -- may be topologically non-trivial. I will explore the use of `spinning tops' to explore this physics. In particular I will discuss an experimental and theoretical study of a simple kind of active meta-material – coupled gyroscopes – that naturally encodes non-trivial topology in its vibrational spectrum. These materials have topologically protected edge modes which we observe in experiment. Crucially, the geometry of the underlying lattice controls the presence of time reversal symmetry that is essential to the non-trivial topology of the spectrum. We exploit this to control the chirality of the edge modes by simply deforming the lattice. Moving beyond ordered lattices we show that amorphous gyroscopic networks are naturally topological. We construct them from arbitrary point sets -- including hyperuniform, jammed, quasi-crystalline and uniformly random -- and control their topology through simple, local decorations.

We will discuss local formulas for K-theory that can be defined on models with irregular boundaries and lattice defects. This form of K-theory can work with models that have sites in real space are random or quasicrystalline. Simple formulas for these finite-volume invariants allow for fast numerics and quantitative statements about the robustness of certain states against disorder.

Resonators couple to each other when put in contact, leading to collective resonant modes. An interesting problem is to understand and exploit these collective modes when the resonators form different patterns in space. In this talk I will first present a kaleidoscope of numerical examples where patterned resonators display spectral properties akin to 2- and higher-dimensional Integer Quantum Hall Effect. In the second part, I will demonstrate how K-theory can be used to understand and predict the bulk and the edge spectrum of such systems. In particular, a simple K-theoretic version of the bulk-boundary principle will be presented which enables one to see when topological edge spectrum is to be expected. This last part will be supported again with a kaleidoscope of numerical examples.

In 2005 Haldane conjectured that topological phenomena were not quantum but wave effects. He proposed [RH08] an electromagnetic analog of the Quantum Hall Effect, something that was confirmed in a number of spectacular experiments [Wan+08; Rec+13] a few years later. These and other, more recent works have naturally raised two questions: (1) How similar is the Quantum Hall Effect for light to the one from solid state physics? And (2) are there other, as-of-yet unknown topological effects in electromagnetic media? The crucial ingredient are symmetries, and when designing topological electromagnetic media, there are two axes to explore: One can choose the materials from which to build the photonic crystal (material symmetries) and then decide how to periodically arrange these materials (crys- tallographic symmetries). For material symmetries we answer both of these questions conclusively by first reformulating Maxwell’s equations in Schrödinger form [DL17], and then adapting the Cartan-Altland-Zirnbauer classification scheme for topological insulators [DL14; DL16]. With regards to question (1), gyrotropic media are in the same symmetry class (class A) as solids exhibiting the Quantum Hall Effect. This is a first step to proving photonic bulk-edge correspon- dences that would make Haldane’s conjecture precise: In a two-dimensional topological photonic crystal the Chern number quantifies the net number of edge modes traveling from left to right. Ques- tion (2) has a negative answer, in dimension d ≤ 3 there are no as-of-yet undiscovered topological effects due to material symmetries. In particular, despite some claims to the contrary, there is no electromagnetic analog of the Quantum Spin Hall Effect as that requires the presence of an odd time-reversal symmetry (a realization of class AII). Acknowledgements M. L. thanks JSPS for support of his research with a WAKATE B grant. G. D. research is supported by the grant Iniciación en Investigación 2015 - No 11150143 funded by FONDECYT.

Among the large variety of complex non-periodic structures, quasicrystals and quasiperiodic distributions play a special role. These structures have some of their physical properties (e.g. dielectric constant, potential, etc.) modulated according to a deterministic non-periodic pattern such as a substitution rules set or a cut & project construction. Such architectures have long been recognized to yield a pronounced long-range order manifesting as an infinite set of crystallographic Bragg peaks and a highly lacunar singular-continuous energy spectrum, with an infinite set of gaps arranged in a multifractal hierarchy. The possibility that such structures also possess distinct topological features has been discussed both in mathematics and physics literature including some descriptions of the spectrum through topological invariants. These topological numbers, emerging from the structural building rules, are known to label the dense set of spectral gaps. We present the topological properties of a finite quasiperiodic chains studied using the scattering and also the diffraction of waves. We show that the topological invariants may be measured from the winding of a chiral scattering phase as a function of a phason structural degree of freedom. Using a Fabry-Perot point of view, this chiral phase is also shown to drive the spectral traverse of conveniently emulated edge states. Furthermore, we present a method to obtain all available topological numbers from the diffraction pattern of a quasicrystal, a method which may be termed topological quasicrystallography. Existing experimental realizations will be addressed, as well as the possible generalizations.

Time-reversal symmetry is a property shared by wave phenomena in linear stationary media. However, broken time-reversal symmetry is required for synthesizing nonreciprocal devices like isolators, circulators, gyrators, and for topological systems supporting chiral states. Magnetic fields can of course enable nonreciprocal behavior for electromagnetic waves, but this method does not conveniently translate to the chip-scale or to the acoustic domain, compelling us to search for nonmagnetic solutions. We have adopted a unique approach to address this challenge through the use of co-localized interacting modes of light and sound in resonator systems. The acousto-optical physics within these systems enable fundamental experiments having analogies to condensed matter phenomena, including phonon laser action [1], cooling [2, 3], and electromagnetically induced transparency [4]. This talk will describe our experimental efforts to exploit the momentum conservation rules intrinsic to light-sound interactions for producing strong nonreciprocal behavior, using both optical and acoustic pumping. We have demonstrated that such ‘nonreciprocal atoms’ can be used to produce complete optical isolation with ultra-low loss over a very compact footprint [5]. Our results also reveal that chiral effects are pervasive throughout the phononic and photonic physical layers of these systems, for instance, showing that chirality can be dynamically imparted to phonon transport to suppress disorder-induced backscattering [6]. This talk will also describe how intuitions drawn from our optomechanical experiments can be used to design practical microwave and acoustic systems with reconfigurable topology and nonreciprocal responses. References 1. G. Bahl, J. Zehnpfennig, M. Tomes, T. Carmon, "Stimulated optomechanical excitation of surface acoustic waves in a microdevice," Nature Communications, 2:403, 2011. 2. G. Bahl, M. Tomes, F. Marquardt, T. Carmon, "Observation of spontaneous Brillouin cooling," Nature Physics, Vol. 8, No. 3, pp. 203-207, 2012. 3. S. Kim, G. Bahl, "Role of optical density of states in two-mode optomechanical cooling," Optics Express 25(2), pp.776-784, 2017. 4. J. Kim, M. Kuzyk, K. Han, H. Wang, G. Bahl, "Non-reciprocal Brillouin scattering induced transparency," Nature Physics, 11, pp. 275-280, 2015. 5. J. Kim, S. Kim, G. Bahl "Complete linear optical isolation at the microscale with ultralow loss," Scientific Reports, 7:1647, 2017. 6. S. Kim, X. Xu, J.M. Taylor, G. Bahl, "Dynamically induced robust phonon transport and chiral cooling in an optomechanical system," Nature Communications 8, 205, 2017.

In this talk I will describe our recent ideas of how to engineer nanostructures that generate topological transport of vibrations. These include situations with explicit time-reversal symmetry breaking (via an optical field with optical vorticity) as well as with time-reversal symmetry intact. In the latter case, I will show how the snowflake phononic crystal, first invented for the purposes of optomechanics, provides an ideal platform in which to implement both pseudomagnetic fields for vibrations as well as a topological insulator. Pseudomagnetic fields for sound at the nanoscale Christian Brendel, Vittorio Peano, Oskar Painter, and Florian Marquardt, Proceedings of the National Academy of Sciences (PNAS) 114, E3390–E3395 (2017) Snowflake Topological Insulator for Sound Waves Christian Brendel, Vittorio Peano, Oskar Painter, and Florian Marquardt, arXiv:1701.06330 (2017) Topological Phases of Sound and Light Vittorio Peano, Christian Brendel, Michael Schmidt, and Florian Marquardt, Phys. Rev. X 5, 031011 (2015)

Abstract- Photonic topological insulators are an interesting class of materials whose photonic band structure can have a band gap in the bulk while supporting topologically protected unidirectional edge modes. Recent studies on bianisotropic metamaterials that emulate the electronic quantum spin Hall effect using its electromagnetic analog are examples of such systems with a relatively simple and elegant design. In this presentation, we present a rotating magnetic dipole antenna, composed of two perpendicularly oriented coils, that can efficiently excite the unidirectional topologically protected surface waves in the bianisotropic metawaveguide (BMW) structure recently realized by T. Ma et al. [Phys. Rev. Lett. 114, 127401 (2015)] despite the fact that the BMW medium does not break time-reversal invariance. In addition to achieving a high directivity, the antenna can be tuned continuously to excite reflectionless edge modes in the two opposite directions at various amplitude ratios. We demonstrate its performance through experiments and compare to simulation results. For details, see Phys. Rev. B 94, 195427 (2016). Acknowledgements, This work was supported by the ONR under Grant No. N000141512134, AFOSR COE Grant FA9550-15-1-0171, and the National Science Foundation under Grant Nos. NSF PHY-1415547; AFOSR FA9550-15-1-0075; ARO W911NF-16-1-0319, and NSF ECCS-1158644.

Weyl points are the key to non-trivial topological phenomena in 3D. I will give several examples: 1) Two Weyl points of same first Chern number form double-weyl points. Examples of double-weyl phonons will be shown in crystalline solids. 2) Two Weyl points of opposite first Chern number form 3D Dirac points. Glide-symmetry protected gapped phase with a single surface Dirac cone can be obtained by gapping 3D Dirac points. It has a Z2 invariant. 3) A Chern crystal of a full 3D gap can be obtained by gapping a Weyl pair. It is characterized by three first Chern numbers. 4) Coupling two Weyl points with helical modulations provides one-way fibers of second Chern number in 4D parameter space.

arXiv:1708.08192 Fundamental differences between fermions and bosons are revealed in their spin and distribution statistics as well as the discrete symmetries they obey (charge, parity and time). While significant progress has been made on fermionic topological phases with time-reversal symmetry, the bosonic counterpart still remains elusive. We present here a spin-1 bosonic topological insulator for light by utilizing a Dirac-Maxwell correspondence. Marking a departure from existing structural photonic approaches which mimic the pseudo-spin-1/2 behavior of electrons, we exploit the integer spin and discrete symmetries of the photon to predict the existence of a distinct bosonic topological phase in continuous media. We introduce the bosonic equivalent of Kramers theorem and topological quantum numbers for light as well as the concept of photonic Dirac monopoles, Dirac strings and skyrmions to underscore the correspondence between Maxwell's and Dirac's equations. We predict that a unique magneto-electric medium with anomalous parity and time-reversal symmetries, if found in nature, will exhibit a gapped Quantum spin-1 Hall bosonic phase. Photons do not possess a conductivity transport parameter which can be quantized (unlike topological electronic systems), but we predict that the helical quantization of symmetry--protected edge states in bosonic topological insulators is amenable to experimental isolation.

I will discuss the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. I will present a solution for the bulk and edge state carrier distributions, which takes into account energy and momentum relaxation through radiative recombination and electron-phonon interactions, as well as coupling to an external fermionic reservoir. The resulting steady state resembles a topological insulator in the Floquet basis. The particle distribution in the Floquet edge modes exhibits a sharp feature akin to the Fermi level in equilibrium systems, while the bulk hosts a small density of excitations. Using these distributions, I will analyze the regimes where edge-state transport can be observed. These results show that signatures of the non-trivial topology persist in the non-equilibrium steady state.

When a small quantum system is subject to multiple periodic drives, it may realize multidimensional topological phases. In my talk, I will explain how to make such constructions, and show how a spin-1/2 particle driven by two elliptically-polarized light beams could realize the Bernevig-Hughes-Zhang model of 2 topological insulators. The observable consequence of such construction is quantized pumping of energy between the two drive sources.

I will present two topics of research in our group related to synthetic topological quantum matter [1]: (i) topological phases in 3D optical lattices, more specifically a proposal for experimental realization of Weyl semimetals in ultracold atomic gases [2], and (ii) anyons [3,4]. I will present one possible route to engineer anyons in a 2D electron gas in a strong magnetic field sandwiched between materials with high magnetic permeability, which induce electron-electron vector interactions to engineer charged flux-tube composites [3]. I will also discuss intriguing concepts related to extracting observables from anyonic wavefunctions [4]: one can show that the momentum distribution is not a proper observable for a system of anyons [4], even though this observable was crucial for the experimental demonstration of Bose-Einsten condensation or ultracold fermions. [1] N. Goldman, G. Juzeliunas, P. Ohberg, I. B. Spielman, Rep. Prog. Phys. 77, 126401 (2014). [2] Tena Dubček, Colin J. Kennedy, Ling Lu, Wolfgang Ketterle, Marin Soljačić, Hrvoje Buljan, Weyl points in three-dimensional optical lattices: Synthetic magnetic monopoles in momentum space, Phys. Rev. Lett. 114, 225301 (2015). [3] M. Todorić, D. Jukić, D. Radić, M. Soljačić, and H. Buljan, The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons, in preparation [4] Tena Dubček, Bruno Klajn, Robert Pezer, Hrvoje Buljan, Dario Jukić, Quasimomentum distribution and expansion of an anyonic gas, arXiv:1707.04712.

Honeycomb lattice plays an important role in the course of fostering topology physics as known from the Haldane model and the Kane-Mele model [1]. Recently, we propose a way to achieve all-dielectric topological photonics starting from honeycomb structure. We identify a pseudospin degree of freedom in electromagnetic (EM) modes hosted by honeycomb lattice, which can be explored for establishing topological EM states with time-reversal symmetry [2]. We demonstrate theoretically the nontrivial topology by showing photonic band inversions, and counter-propagating edge EM waves. I will show recent experimental results of microwaves which confirm our theory [3]. The idea can also be applied for electronic systems [4]. In terms of the tight-binding model on honeycomb lattice with detuned nearest-neighbor hopping, we find that the topological state is characterized by mirror winding numbers, and absence of the so-called minigap in the edge states can be shown analytically [5]. Recent progresses and perspectives of the present approach will be discussed. References: [1] H.-M. Weng, R. Yu, X. Hu, X. Dai and Z. Fang, Adv. Phys. vol. 64, 227 (2015). [2] L.-H. Wu and X. Hu: Phys. Rev. Lett. vol. 114, 223901 (2015). [3] Y.-T. Yang, J.-H. Jiang, X. Hu and Z.-H. Hang: arXiv.1610.07780. [4] L.-H. Wu and X. Hu: Sci. Rep. vol. 6, 24347 (2016). [5] T. Kariyado and X. Hu: arXiv.1607.08706.

The group Waves in complex systems in Nice (France) is interested in controlling the wave transport properties in various systems whose mastered designs range from homogeneous systems with complex geometries to either periodic or disordered structured materials. Thanks to an experimental versatile platforms in microwaves, we develop recently analog approaches of topological effects in condensed matter, and more specifically in 1D or 2D periodic or quasiperiodic (meta-)materials. I will give a review of some of our results ranging from the observation of a topological phase transition in strained artificial graphene to intuitive physical interpretation of the gap-labelling in a Penrose tilling.

In this talk we will discuss some recent experiments with photonic lattices done at the Institute of Photonics and Quantum Sciences in Edinburgh, UK. In particular the work with slowly driven lattices where non-trivial topological phenomena can be observed will be presented. We will also discuss some recent, perhaps rather speculative, theoretical ideas on how to create long-range interactions based on non-local photon fluids.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.