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

Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.

https://science.sciencemag.org/content/sci/349/6250/842.full.pdf

Observation of many-body localization of interacting fermions in a quasirandom optical lattice

Anderson localization of waves in disordered media was originally predicted fifty years ago, in the context of transport of electrons in crystals. The phenomenon is much more general and has been observed in a variety of systems, including light waves. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice-a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases.

/pdf/anderson-localization-of-a-non-interacting-bose-einstein-1kwmtoh7kq.pdf

Anderson localization of a non-interacting Bose-Einstein condensate.

Anderson localization (AL) is a phenomenon in wave physics, occurring when interference between multiple scattering paths causes diffusion to cease. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases, but there has been no direct observation of AL for matter waves of any type. The paper reports AL in a Bose–Einstein condensate as it expands in a one-dimensional disordered optical potential. The authors image directly the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary exponentially localized wave function — a direct signature of AL. The method can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions. In 1958, Anderson predicted the localization1 of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics2 because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves3,4,5,6,7, microwaves8,9, sound waves10 and electron gases11. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose–Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle12. We operate in a regime of pure Anderson localization, that is, with weak disorder—such that localization results from many quantum reflections of low amplitude—and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction—a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

Direct observation of Anderson localization of matter waves in a controlled disorder

Here, we will first briefly summarize the general principles of QD synthesis using our previous work on InP as an example. Then we will focus on QDs of the IV-VI Pb chalcogenides (PbSe, PbS, and PbTe) and Si QDs because these were among the first QDs that were reported to produce multiple excitons upon absorbing single photons of appropriate energy (a process we call multiple exciton generation (MEG)). We note that in addition to Si and the Pb-VI QDs, two other semiconductor systems (III-V InP QDs(56) and II-VI core-shell CdTe/CdSe QDs(57)) were very recently reported to also produce MEG. Then we will discuss photogenerated carrier dynamics in QDs, including the issues and controversies related to the cooling of hot carriers and the magnitude and significance of MEG in QDs. Finally, we will discuss applications of QDs and QD arrays in novel quantum dot PV cells, where multiple exciton generation from single photons could yield significantly higher PV conversion efficiencies.

/pdf/semiconductor-quantum-dots-and-quantum-dot-arrays-and-4c2cspcqy1.pdf

Semiconductor quantum dots and quantum dot arrays and applications of multiple exciton generation to third-generation photovoltaic solar cells.

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one-dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhance localization in one type and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of delta-like wave packets in the presence of disorder. A transition from ballistic wave packet expansion to exponential (Anderson) localization is observed. We also find an intermediate regime in which the ballistic and localized components coexist while diffusive dynamics is absent. Evidence is found for a faster transition into localization under nonlinear conditions.

/pdf/anderson-localization-and-nonlinearity-in-one-dimensional-16cuqk4880.pdf

Anderson localization and nonlinearity in one-dimensional disordered photonic lattices.

We experimentally investigate carrier multiplication (CM) in type II CdTe/CdSe quantum dot (QD) heterostructures by the means of a simple and robust subnanosecond transient photoluminescence spectroscopy setup. Experimental conditions were set to minimize the blurring of the CM signature by extraneous effects. The extracted photon energy threshold for CM is consistent with previous studies in CdSe and CdTe QDs (around 2.65 times the type II energy band gap) and we can infer an upper bound to CM yield. This study indicates that, while CM is probably present in type II QD heterostructures below the CM threshold for each constituent separately, it exhibits only a modest yield.

An upper bound to carrier multiplication efficiency in type II colloidal quantum dots.

The exciton-exciton interaction energy of tellurium doped CdSe colloidal quantum dots is experimentally investigated. The dots exhibit a strong Coulomb repulsion between the two excitons, which results in a huge measured biexciton blue shift of up to 300 meV. Such a strong Coulomb repulsion implies a very narrow hole wave function localized around the defect, which is manifested by a large Stokes shift. Moreover, we show that the biexciton blue shift increases linearly with the Stokes shift. This result is highly relevant for the use of colloidal QDs as optical gain media, where a large biexciton blue shift is required to obtain gain in the single exciton regime.

Large blue shift of the biexciton state in tellurium doped CdSe colloidal quantum dots.

The exciton-exciton interaction energy of Tellurium doped CdSe colloidal quantum dots is experimentally investigated. The dots exhibit a strong Coulomb repulsion between the two excitons, which results in a huge measured biexciton blue shift of up to 300 meV. Such a strong Coulomb repulsion implies a very narrow hole wave function localized around the defect, which is manifested by a large Stokes shift. Moreover, we show that the biexciton blue shift increases linearly with the Stokes shift. This result is highly relevant for the use of colloidal QDs as optical gain media, where a large biexciton blue shift is required to obtain gain in the single exciton regime.

A Large Blue Shift of the Biexciton State in Tellurium Doped CdSe Colloidal Quantum Dots

The energetics and dynamics of multiply excited states in single material colloidal quantum dots have already been shown to exhibit universal trends. Here we attempt to identify similar trends in exciton–exciton interactions within compound colloidal quantum dots. For this end, we thoroughly review previously available data and also present experimental data on several newly synthesized systems, focusing on core/shell nanocrystals with a type-II band alignment. A universal condition for the transition from binding to repulsion of the biexciton (type-I–type-II transition) is established in terms of the change in the exciton radiative lifetime. A scaling rule is also presented for the magnitude of exciton–exciton repulsion. In contrast, we do not identify a clear universal scaling of the non-radiative Auger recombination lifetime of the biexciton state. Finally, a perspective on future applications of engineered multiexcitonic states is presented.

Assaf Avidan

Papers

Anderson localization and nonlinearity in one-dimensional disordered photonic lattices.

An upper bound to carrier multiplication efficiency in type II colloidal quantum dots.

Large blue shift of the biexciton state in tellurium doped CdSe colloidal quantum dots.

A Large Blue Shift of the Biexciton State in Tellurium Doped CdSe Colloidal Quantum Dots

Energetics and dynamics of exciton–exciton interactions in compound colloidal semiconductor quantum dots