There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

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.

Topological Photonics

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

In this paper, we developed an efficient method for searching the resonant eigenfrequency of dielectric optical microcavities by the boundary element method. By transforming the boundary integral equation to a general eigenvalue problem for arbitrary, symmetric, and multi-domain shaped optical microcavities, we analyzed the regular motion of the eigenvalues against the frequency. The new strategy can predict multiple resonances, increase the speed of convergence, and avoid non-physical spurious solutions. These advantages greatly reduce the computation time in the search process of the resonances. Moreover, this method is not only valuable for dielectric microcavities, but is also suitable for other photonic systems with dissipations, whose resonant eigenfrequencies are complex numbers.

Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

Efficient phase manipulation of light is the cornerstone of many advanced photonic applications1–4. However, the pursuit of compact, broadband and deep phase control of light has been hindered by the finite nonlinearity of the optical materials available for integrated photonics5,6. Here, we propose a dynamically driven photonic structure for deep phase manipulation and coherent spectrotemporal control of light based on distributed nanomechanics. We experimentally demonstrate the quasi-phase-matched interaction between stationary mechanical vibration and itinerant optical fields, which is used to generate an on-chip modulated frequency comb over 1.15 THz (160 lines), corresponding to a phase modulation depth of over 21.6π. In addition, an optical time-lens effect induced by mechanical vibration is realized, leading to optical pulse compression of over 70-fold to obtain a minimum pulse duration of 1.02 ps. The high efficiency and versatility make such mechanically driven dynamic photonic structures ideal for realizing complex optical control schemes, such as lossless non-reciprocity7, frequency division optical communication1 and optical frequency comb division8. Optomechanical coupling enables an on-chip frequency comb and optical time-lens for 70-fold optical pulse compression.

Spectrotemporal shaping of itinerant photons via distributed nanomechanics

Superconducting cavity electro-optics presents a promising route to coherently convert microwave and optical photons and distribute quantum entanglement between superconducting circuits over long-distance. Strong Pockels nonlinearity and high-performance optical cavity are the prerequisites for high conversion efficiency. Thin-film lithium niobate (TFLN) offers these desired characteristics. Despite significant recent progresses, only unidirectional conversion with efficiencies on the order of 10−5 has been realized. In this article, we demonstrate the bidirectional electro-optic conversion in TFLN-superconductor hybrid system, with conversion efficiency improved by more than three orders of magnitude. Our air-clad device architecture boosts the sustainable intracavity pump power at cryogenic temperatures by suppressing the prominent photorefractive effect that limits cryogenic performance of TFLN, and reaches an efficiency of 1.02% (internal efficiency of 15.2%). This work firmly establishes the TFLN-superconductor hybrid EO system as a highly competitive transduction platform for future quantum network applications. Coherent conversion between optical and microwave photonics is needed for future quantum applications. Here, the authors combine thin-film lithium niobate and superconductor platforms as a hybrid electro-optic system to achieve high-efficiency frequency conversion between microwave and optical modes.

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Bidirectional interconversion of microwave and light with thin-film lithium niobate.

High-Qplasmonic and dielectric modes in a metal-coated whispering-gallery microcavity

The unconditional squeezing of the collective spins of an atomic ensemble in a laser driven optical cavity [I. D. Leroux, M. H. Schleier-Smith, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett 104, 073602 (2010)] is studied and analyzed theoretically. Surprisingly, we find that the largely detuned driving laser can improve the scaling of cavity squeezing from ${S}^{\ensuremath{-}2/5}$ to ${S}^{\ensuremath{-}2/3}$, where $S$ is the total atomic spin. Moreover, we also demonstrate that the experimental imperfection of photon scattering into free space can be efficiently suppressed by detuning.

Chang-Ling Zou

Papers

Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

Spectrotemporal shaping of itinerant photons via distributed nanomechanics

Bidirectional interconversion of microwave and light with thin-film lithium niobate.

High-Qplasmonic and dielectric modes in a metal-coated whispering-gallery microcavity

Detuning-enhanced cavity spin squeezing