Photonic circuits, in which beams of light redirect the flow of other beams of light, are a long-standing goal for developing highly integrated optical communication components1,2,3. Furthermore, it is highly desirable to use silicon—the dominant material in the microelectronic industry—as the platform for such circuits. Photonic structures that bend, split, couple and filter light have recently been demonstrated in silicon4,5, but the flow of light in these structures is predetermined and cannot be readily modulated during operation. All-optical switches and modulators have been demonstrated with III–V compound semiconductors6,7, but achieving the same in silicon is challenging owing to its relatively weak nonlinear optical properties. Indeed, all-optical switching in silicon has only been achieved by using extremely high powers8,9,10,11,12,13,14,15 in large or non-planar structures, where the modulated light is propagating out-of-plane. Such high powers, large dimensions and non-planar geometries are inappropriate for effective on-chip integration. Here we present the experimental demonstration of fast all-optical switching on silicon using highly light-confining structures to enhance the sensitivity of light to small changes in refractive index. The transmission of the structure can be modulated by up to 94% in less than 500 ps using light pulses with energies as low as 25 pJ. These results confirm the recent theoretical prediction16 of efficient optical switching in silicon using resonant structures.

All-optical control of light on a silicon chip

Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent atomic orbitals in an electronic wave function, which uncovers the unconventional Mott insulating state induced by relativistic spin-orbit coupling in the layered 5d transition metal oxide Sr2IrO4. A selection rule based on intra-atomic interference effects establishes a complex spin-orbital state represented by an effective total angular momentum = 1/2 quantum number, the phase of which can lead to a quantum topological state of matter.

http://science.sciencemag.org/content/sci/323/5919/1329.full.pdf

Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4.

We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

/pdf/electrodynamics-of-correlated-electron-materials-2qg1x9aaaz.pdf

Electrodynamics of correlated electron materials

Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high-temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering in both the visible (Raman effect) and x-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectroscopy, and other transport and thermodynamic measurements in correlated materials. Particular focus will be placed on photon polarizations and the role of symmetry to elucidate the dynamics of electrons in different regions of the Brillouin zone. This advantage over conventional transport (usually measuring averaged properties) provides new insights into anisotropic and complex many-body behavior of electrons in various systems. Recent developments in the theory of electronic Raman scattering in correlated systems and experimental results in paradigmatic materials such as the A15 superconductors, magnetic and paramagnetic insulators, compounds with competing orders, as well as the cuprates with high superconducting transition temperatures are reviewed. An overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders is presented. In a variety of materials, observations which may be understood and a summary of important open questions that pave the way to a detailed understanding of correlated electron systems, are discussed.

/pdf/inelastic-light-scattering-from-correlated-electrons-3u08u0719o.pdf

Inelastic light scattering from correlated electrons

Quantum entanglement in condensed matter systems

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T(c)) superconductors is one of the deepest problems in condensed matter physics. One candidate is the 'stripe' phase, in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the 'spin ladder', which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high-T(c) material with lower dimensionality, and has been predicted to exhibit both superconductivity and an insulating 'hole crystal' phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high-T(c) materials. Here we report the existence of a hole crystal in the doped spin ladder of Sr14Cu24O41 using a resonant X-ray scattering technique. This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions, and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.

https://arxiv.org/pdf/cond-mat/0501087.pdf

Crystallization of charge holes in the spin ladder of Sr14Cu24O41.

An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO2 plane is uniform or inhomogeneous. Because the carriers comprise a small fraction of the total charge density and may be rapidly fluctuating, modulations are difficult to detect directly. We demonstrate that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times. This enhances diffraction from the doped holes by more than 10(3), permitting direct structural analysis of the superconducting ground state. Scattering from thin films of La2CuO4+delta (superconducting transition temperature = 39 K) at temperature = 50 +/- 5 kelvin on the reciprocal space intervals (0,0,0.21) --> (0,0,1.21) and (0,0,0.6) --> (0.3,0,0.6) shows a rounding of the carrier density near the substrate suggestive of a depletion zone or similar effect. The structure factor for off-specular scattering was less than 3 x 10(-7) electrons, suggesting an absence of in-plane hole ordering in this material.

https://science.sciencemag.org/content/sci/297/5581/581.full.pdf

A structural probe of the doped holes in cuprate superconductors

We have utilized resonant x-ray diffraction at the Mn L(II,III) edges in order to directly compare magnetic and orbital correlations in Pr(0.6)Ca(0.4)MnO(3). Comparing the widths of the magnetic and orbital diffraction peaks, we find that the magnetic correlation length exceeds that of the orbital order by nearly a factor of 2. Furthermore, we observe a large (similar to3 eV) spectral weight shift between the magnetic and orbital resonant line shapes, which cannot be explained within the classic Goodenough picture of a charge-ordered ground state. To explain the shift, we calculate the orbital and magnetic resonant diffraction line shapes based on a relaxed charge-ordered model.

https://arxiv.org/pdf/cond-mat/0311553.pdf

Soft x-ray resonant diffraction study of magnetic and orbital correlations in a manganite near half doping

We report direct evidence of charge/orbital ordering of low energy electronic states of $Cu$ in YBa$_2$Cu$_3$O$_{6+x}$ ortho-II phase in both the $CuO_3$ chain and the CuO$_2$ plane. Huge enhancement of the $({1/2},0,0)$ superstructure Bragg peak is observed when photon energy is tuned to the $Cu L_{2,3}$ absorption edge with large polarization dependence. The ordering in the $CuO_2$ plane discovered here sheds new light on how the one dimensional $Cu-O$ chains affect the $CuO_2$ plane, and why many normal and superconducting state properties of this system exhibit strong anisotropy.

https://arxiv.org/pdf/cond-mat/0402488.pdf

Zooming-in on the charge ordering in YBa2Cu3O6.5

/pdf/a-structural-probe-of-the-doped-holes-in-the-cuprates-hoojlwhlcp.pdf

L. Venema

Papers

Crystallization of charge holes in the spin ladder of Sr14Cu24O41.

A structural probe of the doped holes in cuprate superconductors

Soft x-ray resonant diffraction study of magnetic and orbital correlations in a manganite near half doping

Zooming-in on the charge ordering in YBa2Cu3O6.5

A Structural Probe of the Doped Holes in the Cuprates