Photonic Floquet topological insulators

Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel K.; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander

doi:10.1038/nature12066

Cited by 2,954 publications

(2,558 citation statements)

References 41 publications

(27 reference statements)

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“…To controllably explore the emergence of these phenomena, efforts have recently focused on realizing synthetic materials in artificial magnetic fields, and in particular, upon implementations for cold atoms and photons. Successful photonic implementations have employed lattices with engineered tunneling [6,[21][22][23][24]. However, it is desirable to realize artificial magnetic fields in the simpler case of a continuum (lattice-free) material [7,25,26], where strong interactions are more easily accessible and the theory maps more directly to fractional quantum Hall systems.…”

mentioning

confidence: 99%

Synthetic Landau levels for photons

Schine

Ryou

Gromov

et al. 2016

Nature

208

243

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Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties [1][2][3][4][5]. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science [6][7][8]. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip [9]. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap [10]. Using spatialand energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit [10,11], we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen-Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space [12][13][14][15]. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids [16,17] and direct detection of anyons [18,19].The Lorentz force on a charged particle moving in a magnetic field leads to the unique topological features of quantum Hall systems, including precisely quantized Hall conductance, topologically protected edge transport, and, in the presence of interactions, the predicted anyonic and non-abelian braiding statistics that form the basis of topological quantum computing [20]. To controllably explore the emergence of these phenomena, efforts have recently focused on realizing synthetic materials in artificial magnetic fields, and in particular, upon implementations for cold atoms and photons. Successful photonic implementations have employed lattices with engineered tunneling [6,[21][22][23][24]. However, it is desirable to realize artificial magnetic fields in the simpler case of a continuum (lattice-free) material [7,25,26], where strong interactions are more easily accessible and the theory maps more directly to fractional quantum Hall systems. In this work, we develop a new approach and demonstrate the first continuum synthetic magnetic field for light.To achieve photonic Landau levels we harness the powerful analogy between photons in a near-degenerate multimode cavity and massive, trapped 2d particles [27,28]. Owing to mirror curvature, the transverse dynamics of a running wave resonator are equivalent to those of a 2D quantum h...

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mentioning

confidence: 99%

Synthetic Landau levels for photons

Schine

Ryou

Gromov

et al. 2016

Nature

208

243

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“…In contrast, in edge-mode guiding systems [11,12,[15][16][17][18], the intensity maximum is located at the edge. This difference is of great importance in practice.…”

Section: Introductionmentioning

confidence: 90%

“…Once a scalable system with individually controllable coupling modulation is conceived, a rich system of arbitrarily engineered effective gauge fields can be realized, providing the potential to explore a wider range of phenomena in gauge-field physics that is difficult to realize in solidstate systems. We also note that similar gauge-field concepts should be experimentally implementable in the optical analogs of topological insulators, where a gauge potential depending on photon spin has been theoretically proposed and experimentally realized [12,13,15,16,26].…”

Section: Final Remarks and Conclusionmentioning

confidence: 99%

“…Photons are neutral particles, and hence there is no naturally existing gauge field that couples to photons. Nevertheless, in recent years, various mechanisms for creating effective gauge field for photons have been proposed [5][6][7][8][9][10][11][12][13][14] and demonstrated [15][16][17]. In particular, it has been pointed out by Fang et al [18] that a photonic gauge field can be created in a dynamically modulated photonic structure by controlling the modulation phase.…”

Section: Introductionmentioning

confidence: 99%

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Light Guiding by Effective Gauge Field for Photons

2014

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We propose a waveguiding mechanism based on the effective gauge potential for photons. The waveguide geometry consists of core and cladding regions with the same underlying dispersion relation, but subject to different gauge potentials. This geometry can be realized in a dynamically modulated resonator lattice and provides a conceptually straightforward and dynamically reconfigurable mechanism for generating a one-way waveguide.

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“…Following the pace of condensed matter, these conical dispersion bands have been extended to bosonic systems particularly for electromagnetic waves [4][5][6][7][8][9][10][11][12] . Bosonic Dirac cones at the zone boundary reveal many similar phenomena with fermionic particles.…”

mentioning

confidence: 99%

Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration

He¹,

Huang²,

Chang³

et al. 2016

ACS Photonics

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Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect without longitudinal spherical aberration, when the size of zero-index lens is large enough. Here, we designed and fabricated a prototype of zero-refractive-index lens by comprising large-area silicon nanopillar array with plane-concave profile. Near-zero refractive index was quantitatively measured near 1.55 m through anomalous focusing effect, predictable by effective medium 2 theory. The zero-index lens was also demonstrated to perform ultralow longitudinal spherical aberration. Such IC compatible device provides a new route to integrate all-silicon zero-index materials into optical communication, sensing, and modulation, and to study fundamental physics on the emergent fields of topological photonics and valley photonics.Dirac cones in fermionic systems have attracted tremendous attention in the fields of topological insulator and graphene [1][2][3] . Following the pace of condensed matter, these conical dispersion bands have been extended to bosonic systems particularly for electromagnetic waves 4-12 . Bosonic Dirac cones at the zone boundary reveal many similar phenomena with fermionic particles. For example, bianisotropic metamaterials can access to modulate the spin flow of light with backscattering immune at the boundary of topological photonic crystals, after opening a nontrivial gap from Dirac cone 13,8,11 . An alternative method is proposed to implement photonic analogue of the integer quantum Hall effect by using periodic coupling resonators on a silicon-on-insulator platform in near-infared (NIR) wavelength scale 7,14,15 .Beyond those predominant behaviors, bosonic Dirac cones also present extra features other than femionic systems. Recently, another type of photonic Dirac cones induced by accidental degeneracy at the zone center has been found in a class of all-dielectric photonic crystals 16,17 , in which the optical response shows very different to the case at the zone boundary. One of the remarkable properties is zero-index behavior such that the effective permittivity and permeability are simultaneously to be zero at Dirac frequency. To date, nanorod-array structure is the exclusive way to realize all-dielectric zero-index photonic crystal in optical frequency regime. How to sufficiently confine the propagation wave in the plane of periodicity is a practical challenge for 3 rod-slab structures. The first implementation at near-infrared (NIR) wavelength has been fabricated by alternating silicon/silica layers ...

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Photonic Floquet topological insulators

Cited by 2,954 publications

References 41 publications

Synthetic Landau levels for photons

Synthetic Landau levels for photons

Light Guiding by Effective Gauge Field for Photons

Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration

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