Photonic Floquet topological insulators
TL;DR: This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.
Abstract: Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrodinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.
Citations
More filters
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.
3,407 citations
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Abstract: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.
3,052 citations
Cites background from "Photonic Floquet topological insula..."
...Finally, gapless surface states were also reported to exist in a bulk hyperbolic metamaterial having bi-anisotropic responses [59]....
[...]
...Much like the field of topological insulators in electronics, topological photonics promises an enormous variety of breakthroughs in both the fundamental physics and the technological outcomes....
[...]
01 Jul 2017
TL;DR: A new architecture for a fully optical neural network is demonstrated that enables a computational speed enhancement of at least two orders of magnitude and three order of magnitude in power efficiency over state-of-the-art electronics.
Abstract: Artificial Neural Networks have dramatically improved performance for many machine learning tasks. We demonstrate a new architecture for a fully optical neural network that enables a computational speed enhancement of at least two orders of magnitude and three orders of magnitude in power efficiency over state-of-the-art electronics.
1,955 citations
Cites background from "Photonic Floquet topological insula..."
...3-D photonic integration could enable even larger ONNs by adding another spatial degree of freedom [44]....
[...]
TL;DR: In this paper, the interplay between parity-time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics has been explored both theoretically and experimentally.
Abstract: In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.
1,831 citations
TL;DR: The experimental realization of the Haldane model and the characterization of its topological band structure are reported, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice and a direct extension to realize spin-dependent topological Hamiltonians is proposed.
Abstract: The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although physical implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report the experimental realization of the Haldane model and the characterization of its topological band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topology of the lowest band, by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topological properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topological Hamiltonians.
1,727 citations
Cites methods from "Photonic Floquet topological insula..."
...Using photonic crystal fibres, a classical version of this proposal was used to study topologically protected edge modes in the inversion-symmetric regime [21]....
[...]
References
More filters
TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
18,958 citations
TL;DR: In this paper, the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topologically insulators have been observed.
Abstract: Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.
15,562 citations
"Photonic Floquet topological insula..." refers background in this paper
...The topological insulator[1] is a new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, and is topologically protected....
[...]
TL;DR: Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
Abstract: We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
6,058 citations
"Photonic Floquet topological insula..." refers background or methods in this paper
...We show this behaviour in beam-propagation-method (BPM) simulations(30), solving equation (1) (see Supplementary Video 1)....
[...]
...The quantum mechanical analogue of equation (1) describes the propagation of a quantum particle that evolves in time—for example, an electron in a solid....
[...]
...Launching a beam into the waveguide at the upper-left corner of the triangle (circled) excites two types of eigenstates: (1) bulk states extending to the corner, and (2) edge states that meet at the corner....
[...]
TL;DR: In this article, the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field effect transistor, was measured and it was shown that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device.
Abstract: Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported.
5,619 citations
TL;DR: In this article, the Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential, where the Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap.
Abstract: The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential $U$. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small $\frac{U}{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}$.
4,811 citations
"Photonic Floquet topological insula..." refers background or methods in this paper
...es: (1) employing bianisotropic metamaterials with strong magnetic response16; (2) using an aperiodic coupled-resonator system that realizes the quantum Hall effect in two uncoupled photonic modes10; (3) by dynamically modulating a two-dimensional photonic crystal structure17 to explicitly break time-reversal symmetry; and (4) by coupling the polarization and propagation degrees of freedom18. However...
[...]
...veguide modes and the presence of the vector potential allow us to describe the propagation of light through the lattice by coupled mode theory: i∂ z" ψ n (z")=c(λ)eiA·r mnψ m (z") m ∑ (3) where the summation is only taken over nearest-neighbor waveguides; ψ n(z’) is the amplitude of the mode in the nth waveguide; c(λ) is the wavelength-dependent coupling constant between waveguides an...
[...]