Two-dimensional topological quantum walks in the momentum space of structured light

D’Errico, Alessio; Cardano, Filippo; Maffei, Maria; Dauphin, Alexandre; Barboza, Raouf; Esposito, Chiara; Piccirillo, Bruno; Lewenstein, Maciej; Massignan, Pietro; Marrucci, Lorenzo

doi:10.1364/optica.365028

Cited by 68 publications

(47 citation statements)

References 59 publications

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“…As described in Section 1, the first spin‐dependent deflector based upon the PBP has been realized for IR wavelengths in metallic nanogratings working in transmission, [ 32 ] see Figure a; later the same functionality in the visible band has been achieved in liquid crystals [ 38,115 ] and in metasurfaces. [ 47 ] Due to the largest birefringence

Δ n

, the metasurfaces are the most compact solution, with thicknesses up to few hundred nanometers.…”

Section: Wavefront Tailoringmentioning

confidence: 99%

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

Jisha

Nolte

Alberucci

2021

Laser & Photonics Reviews

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Geometric phase is a unifying and central concept in physics, including optics. As a matter of fact, optics played a pivotal role from the inception of this new paradigm, as some of the first experimental demonstrations have been carried out in optics. A specific type of geometric phase was first introduced by Pancharatnam while investigating interference effects between different polarizations. This specific type of geometric phase, nowadays called the Pancharatnam–Berry phase, is related to the variation of light polarization, encompassing exotic properties when compared with the dynamic phase associated with the optical path. The most widespread manifestation of the Pancharatnam–Berry phase occurs in the presence of a twisted anisotropic material, yielding a point‐wise phase modulation proportional to the local rotation angle of the material. Here the basic mechanism behind the Pancharatnam–Berry phase is discussed. The various applications of this relatively original concept in photonics are then reviewed, presenting both the most important results and manufactured devices reported in literature. The interplay between geometric phase and diffraction occurring in bulk structures is discussed in detail. In the latter case it is shown how geometric phase can be harnessed to generate a new kind of optical waveguide without the necessity of any index gradient.

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Δ n

, the metasurfaces are the most compact solution, with thicknesses up to few hundred nanometers.…”

Section: Wavefront Tailoringmentioning

confidence: 99%

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

Jisha

Nolte

Alberucci

2021

Laser & Photonics Reviews

View full text Add to dashboard Cite

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“…In particular, the formulation of QWs is very suitable for realization in photonic platforms [108]. In the various experiments of photonic QWs, the dynamic of the walker has been encoded in the degrees of freedom of single photon states, such as the polarization for the coin subspace and, for the walker's position, the optical path in bulk [109,110] and integrated interferometers [111][112][113][114][115][116], the time arrival to the detector [117], the modes supported by a multimode fiber [118], the angular [119][120][121], and the transverse momentum [122].…”

Section: Quantum Walksmentioning

confidence: 99%

Transverse and Quantum Localization of Light: A Review on Theory and Experiments

et al. 2021

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Anderson localization is an interference effect yielding a drastic reduction of diffusion—including complete hindrance—of wave packets such as sound, electromagnetic waves, and particle wave functions in the presence of strong disorder. In optics, this effect has been observed and demonstrated unquestionably only in dimensionally reduced systems. In particular, transverse localization (TL) occurs in optical fibers, which are disordered orthogonal to and translationally invariant along the propagation direction. The resonant and tube-shaped localized states act as micro-fiber-like single-mode transmission channels. Since the proposal of the first TL models in the early eighties, the fabrication technology and experimental probing techniques took giant steps forwards: TL has been observed in photo-refractive crystals, in plastic optical fibers, and also in glassy platforms, while employing direct laser writing is now possible to tailor and “design” disorder. This review covers all these aspects that are today making TL closer to applications such as quantum communication or image transport. We first discuss nonlinear optical phenomena in the TL regime, enabling steering of optical communication channels. We further report on an experiment testing the traditional, approximate way of introducing disorder into Maxwell’s equations for the description of TL. We find that it does not agree with our findings for the average localization length. We present a new theory, which does not involve an approximation and which agrees with our findings. Finally, we report on some quantum aspects, showing how a single-photon state can be localized in some of its inner degrees of freedom and how quantum phenomena can be employed to secure a quantum communication channel.

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“…QW protocols have already led to several experimental realizations in 1d with trapped atoms [17], single photons [18], or Bose-Einstein condensates in momentum space [19]. In 2d, a generalization has been done with light [20], and the tentative addition of a magnetic field has also been discussed [21][22][23][24]. We consider a QW in a perpendicular magnetic field and study cage effects on two periodic graphs: (i) the DC with fourfold-coordinated "hub" sites a and twofold "rim" sites (b, c) (Fig.…”

Section: Magnetic Quantum Walksmentioning

confidence: 99%

Tunable Aharonov-Bohm-like cages for quantum walks

2020

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Aharonov-Bohm cages correspond to an extreme confinement for two-dimensional tight-binding electrons in a transverse magnetic field. When the dimensionless magnetic flux per plaquette f equals a critical value f c = 1/2, a destructive interference forbids the particle to diffuse away from a small cluster. The corresponding energy levels pinch into a set of highly degenerate discrete levels as f → f c . We show here that cages also occur for discrete-time quantum walks on either the diamond chain or the T 3 tiling but require specific coin operators. The corresponding quasienergies versus f result in a Floquet-Hofstadter butterfly displaying pinching near a critical flux f c and that may be tuned away from 1/2. The spatial extension of the associated cages can also be engineered.

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Two-dimensional topological quantum walks in the momentum space of structured light

Cited by 68 publications

References 59 publications

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

Transverse and Quantum Localization of Light: A Review on Theory and Experiments

Tunable Aharonov-Bohm-like cages for quantum walks

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