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

Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Quantum information with Rydberg atoms

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

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.

Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems (similar to 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.

/pdf/realization-of-quantum-walks-with-negligible-decoherence-in-isosjbikg6.pdf

Realization of quantum walks with negligible decoherence in waveguide lattices.

We report the observation of the signature of a localization phase transition for light in one-dimensional quasiperiodic photonic lattices, by directly measuring wave transport inside the lattice. Below the predicted transition point an initially narrow wave packet expands as it propagates, while above the transition expansion is fully suppressed. In addition, we measure the effect of focusing nonlinear interaction on the propagation and find it increases the width of the localized wave packets.

Observation of a localization transition in quasiperiodic photonic lattices.

We investigate the effect of nonlinearity in a system described by an adiabatically evolving Hamiltonian. Experiments are conducted in a three-core waveguide structure that is adiabatically varying with distance, in analogy to the stimulated Raman adiabatic passage process in atomic physics. In the linear regime, the system exhibits an adiabatic power transfer between two waveguides which are not directly coupled, with negligible power recorded in the intermediate coupling waveguide. In the presence of nonlinearity the adiabatic light passage is found to critically depend on the excitation power. We show how this effect is related to the destruction of the dark state formed in this configuration.

Effect of nonlinearity on adiabatic evolution of light.

The design and operation of a novel dual-wavelength laterally coupled (LC) distributed feedback (DFB) semiconductor laser are reported. The laser has two different grating periods, one on each sidewall. Stable dual-mode emission, with low threshold currents and good extinction ratio approaching 30 dB, has been demonstrated. Generation of millimeter-wave signals by photomixing has been performed, and the linewidths of each of the individual modes and of the beat mode have been measured as a function of the injection current. It is observed that while the linewidth of the separate modes has a modest dependence on the injection level, the linewidth of the beat mode experiences a strong decrease as the injected current increases

F. Pozzi

Papers

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

Realization of quantum walks with negligible decoherence in waveguide lattices.

Observation of a localization transition in quasiperiodic photonic lattices.

Effect of nonlinearity on adiabatic evolution of light.

Dual-Wavelength InAlGaAs–InP Laterally Coupled Distributed Feedback Laser