Observation of topologically protected bound states in photonic quantum walks

Kitagawa, Takuya; Broome, Matthew A.; Fedrizzi, Alessandro; Rudner, Mark S.; Berg, Erez; Kassal, Ivan; Aspuru‐Guzik, Alán; Demler, Eugene; White, A. G.

doi:10.1038/ncomms1872

Cited by 573 publications

(504 citation statements)

References 29 publications

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“…For the full reconstruction of the Berry curvature, it is necessary to differentiate the measured integrated Berry curvature with respect to the time step m as discussed in equation (14). Directly before evaluating the derivative, a moving average filter is applied to the data to decrease the noise level.…”

Section: Methodsmentioning

confidence: 99%

“…In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals [9][10][11] , propagating waveguides 12 and silicon ring resonators 15,16 . However, while the existence of such edge states is linked to the non-trivial global topological properties of bulk bands, a direct measurement of the Berry curvature itself has so far not been realized.…”

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confidence: 99%

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Experimental measurement of the Berry curvature from anomalous transport

et al. 2017

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The geometric properties of energy bands underlie fascinating phenomena in many systems, including solid-state, ultracold gases and photonics. The local geometric characteristics such as the Berry curvature 1 can be related to global topological invariants such as those classifying the 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 semi-classical evolution of a coherent wavepacket. Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time evolution of a wavepacket in a one-dimensional geometric 'charge' pump, where the Berry curvature leads to an anomalous displacement of the wavepacket. This is both the first direct observation of Berry curvature e ects in an optical system, and a proof-ofprinciple demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.The Berry curvature is a geometrical property of an energy band, which plays a key role in many physical phenomena as it encodes how eigenstates evolve as a local function of parameters 1 . In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 . As first explained by Thouless 3 , there can be an analogous topological quantization of particle transport in a 1D band insulator, when the lattice potential is 'pumped' , that is, is slowly and periodically modulated in time. Also in this case, the geometrical and topological properties are defined for an effective 2D parameter space, but now one spanned by the 1D Bloch momentum and the external periodic pumping parameter.A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps, regardless of whether the global topological Chern number is non-trivial. In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 . As highlighted further below, this anomalous transport can be understood physically as the Berry curvature acting like a magnetic field in parameter space [5][6][7] .In recent years, there have been many landmark experiments to engineer and study geometrical and topological energy bands in ultracold gases and photonics . In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals 9-11 , propagating waveguides 12 and silico...

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

Experimental measurement of the Berry curvature from anomalous transport

et al. 2017

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“…Novel systems, like ultracold atomic gases under suitably designed optical and/or magnetic field configurations [6], and photons in properly designed structures [7], allow for a great flexibility and control of the system Hamiltonian. Even though particles without a magnetic moment cannot experience the usual SO coupling, the engineering of an effective Hamiltonian acting on photons in structured media has led, for instance, to the observation of the photonic analogue of the spin-Hall effect in planar structures [8,9] and in metasurfaces [10], and unidirectional photon transport in lattices with topological protection from disorder scattering [11][12][13]. Effective SO couplings have been induced in arrays of photonic ring resonators using the spinlike degree of freedom associated with the rotation direction of photons in the resonator [13,14].…”

Section: Introductionmentioning

confidence: 99%

Spin-Orbit Coupling for Photons and Polaritons in Microstructures

et al. 2015

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We use coupled micropillars etched out of a semiconductor microcavity to engineer a spin-orbit Hamiltonian for photons and polaritons in a microstructure. The coupling between the spin and orbital momentum arises from the polarization-dependent confinement and tunneling of photons between adjacent micropillars arranged in the form of a hexagonal photonic molecule. It results in polariton eigenstates with distinct polarization patterns, which are revealed in photoluminescence experiments in the regime of polariton condensation. Thanks to the strong polariton nonlinearities, our system provides a photonic workbench for the quantum simulation of the interplay between interactions and spin-orbit effects, particularly when extended to two-dimensional lattices.

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“…For example, graphene under circularly-polarized light changes its band structure into topologically nontrivial one, and shows (interger) quantum Hall effect [6,7]. Photonic quantum-walk systems are also investigated from this viewpoint [8], whose topological phases are experimentally realized [9].…”

Section: Introductionmentioning

confidence: 99%

Dynamically Induced Topological Properties in Two-Dimensional Optical Lattices

Nakagawa

Kawakami²

2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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Topological properties of matter are one of hot topics in condensed matter physics. Recently, these concepts are extended to non-equilibrium systems, especially periodically driven systems. Here we study such non-equilibrium topological quantum phenomena in cold atomic systems in twodimensional optical lattices. First we show results on non-interacting atoms, and then focus on interaction effects on the non-equilibrium topological phases based on time-dependent Schrieffer-Wolfftype perturbation theory.

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Observation of topologically protected bound states in photonic quantum walks

Cited by 573 publications

References 29 publications

Experimental measurement of the Berry curvature from anomalous transport

Experimental measurement of the Berry curvature from anomalous transport

Spin-Orbit Coupling for Photons and Polaritons in Microstructures

Dynamically Induced Topological Properties in Two-Dimensional Optical Lattices

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