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

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.

Parity–time-symmetric whispering-gallery microcavities

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

This paper was published on 8 June 2001 with errors. On page 4, right-hand column, Eqs. 30 and 31 should read as P 0 / =g0 /2u0 and Q 0 / = f0 /2u0, respectively. These errors propagate into the subsequent formulas for the phase shifts, so that on page 5, right-hand column, Eqs. 40 and 41 should read as A= 2 B0 /2u0 /c and B=− 2 A0 /2u0 /c, respectively. Since the difference originates from u0, a constant quantity characterizing the condensate background determined by fixed system parameters, discussions and conclusions of the original paper remain valid. PHYSICAL REVIEW A 79, 049901 E 2009

Erratum: Dark solitons and their head-on collisions in Bose-Einstein condensates [Phys. Rev. A 64, 013617 (2001)]

Envelope-kink phonon localized modes in a homogeneous anharmonic chain

The nonlinear evolution equations for three-wave resonances including intrapulse dispersion are solved by a special ansatz. Several types of three-wave solitary waves and kink solutions are provided explicitly.

Exact solitary wave solutions of three-wave interaction equations with dispersion

The resonant interaction between collective modes in a quasi-one-dimensional (Q1D) attractive Bose–Einstein condensate (BEC) is considered. Nonlinearly coupled amplitude equations are derived using a method of multiple scales. Coupling matrix elements describing mode–mode resonances in both Landau and Beliaev mechanisms are calculated analytically. In particular, second-harmonic generation and three-mode resonant interaction of the collective modes in Q1D BEC are investigated in detail. The result shows that the physics of the resonant mode couplings in attractive Q1D BEC is richer than that of repulsive Q1D BEC.

Resonant Interactions of Collective Modes in a Quasi-One-Dimensional Attractive Bose-Einstein Condensate

A head-on collision between two solitary waves from opposite directions in a Rayleigh-B\'enard convecting fluid is investigated by use of the Poincar\'e-Lighthill-Kuo method. The fluid system is bounded below by an isothermic plane and above a free deformable surface on which a heat flux is fixed. The results show that, near the transition of the long-wavelength oscillatory instability, the solitary waves emerging from the collision can preserve their original identities to the second order. The phase shifts due to the collision are calculated explicitly.

Guoxiang Huang

Papers

Erratum: Dark solitons and their head-on collisions in Bose-Einstein condensates [Phys. Rev. A 64, 013617 (2001)]

Envelope-kink phonon localized modes in a homogeneous anharmonic chain

Exact solitary wave solutions of three-wave interaction equations with dispersion

Resonant Interactions of Collective Modes in a Quasi-One-Dimensional Attractive Bose-Einstein Condensate

Head-on collision between two solitary waves in a Rayleigh-Bénard convecting fluid.