Topological features - global properties not discernible locally - emerge in systems from liquid crystals to magnets to fractional quantum Hall systems. Deeper understanding of the role of topology in physics has led to a new class of matter: topologically - ordered systems. The best known examples are quantum Hall effects, where insensitivity to local properties manifests itself as conductance through edge states that is insensitive to defects and disorder. Current research in engineering topological order primarily focuses on analogies to quantum Hall systems, where the required magnetic field is synthesized in non-magnetic systems. Here, we realize synthetic magnetic fields for photons at room temperature, using linear Silicon photonics. We observe, for the first time, topological edge states of light in a two - dimensional system and show their robustness against intrinsic and introduced disorder. Our experiment demonstrates the feasibility of using photonics to realize topological order in both the non-interacting and many-body regimes

The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest themselves as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and the quantized polarization, from dipole to multipole moments [1][2][3][4]. Here, we demonstrate the first photonic realization of the quantized quadrupole topological phase, using silicon photonics. In this 2nd-order topological phase, the quantization of the bulk quadrupole moment in a two-dimensional system manifests as topologically robust corner states. We unambiguously show the presence of localized corner states and establish their robustness against certain defects. Furthermore, we contrast these topological states against topologically-trivial corner states, in a system without bulk quadrupole moment, and observe no robustness. Our photonic platform could enable the development of robust on-chip classical and quantum optical devices with higher-order topological protection. arXiv:1812.09304v2 [physics.optics]

Electronic transport is localized in low-dimensional disordered media. The addition of gauge fields to disordered media leads to fundamental changes in the transport properties. We implement a synthetic gauge field for photons using silicon-on-insulator technology. By determining the distribution of transport properties, we confirm that waves are localized in the bulk and localization is suppressed in edge states. Our system provides a new platform for investigating the transport properties of photons in the presence of synthetic gauge fields.

Quantum light is characterized by distinctive statistical distributions that are possible only because of quantum mechanical effects. For example, single photons and correlated photon pairs exhibit photon number distributions with variance lower than classically allowed limits. This enables high-fidelity transmission of quantum information and sensing with lower noise than possible with classical light sources. Most quantum light sources rely on spontaneous parametric processes such as down-conversion and four-wave mixing. These processes are mediated by vacuum fluctuations of the electromagnetic field. Therefore, by manipulating the electromagnetic mode structure, for example with dispersion-engineered nanophotonic systems, the spectrum of generated photons can be controlled. However, disorder, which is ubiquitous in nanophotonic fabrication, causes device-to-device spectral variations. Here we realize topologically robust electromagnetic modes and use their vacuum fluctuations to create a quantum light source in which the spectrum of generated photons is much less affected by fabrication-induced disorder. Specifically, we use the topological edge states realized in a two-dimensional array of ring resonators to generate correlated photon pairs by spontaneous four-wave mixing and show that they outperform their topologically trivial one-dimensional counterparts in terms of spectral robustness. We demonstrate the non-classical nature of the generated light and the realization of a robust source of heralded single photons by measuring the conditional antibunching of photons, that is, the reduced likelihood of photons arriving together compared to thermal or laser light. Such topological effects, which are unique to bosonic systems, could pave the way for the development of robust quantum photonic devices.

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary [1,2]. The chirality of edge modes is a consequence of topological character of the bulk. For example, in a non-interacting quantum Hall (QH) model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk-boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number [3]. Here, for the first time, we measure the winding number in a two-dimensional (2D) photonic system. By inserting a unit flux quantum to the edge, we show that the edge spectrum resonances shift by the winding number.This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.Recently, there has been a surge of interest in investigating topological states with synthetic gauge fields.Synthetic gauge fields have been realized in various atomic [4][5][6][7] and photonic systems [8, 9]. In particular, topological photonic edge states have been imaged in two recent concurrent experiments [10,11] [3]. In fermionic systems, conductance measurements reveal these quantum numbers. However, a direct measurement of these integers is non-trivial in bosonic systems, mainly because the concept of conductance is not well defined [23,24]. While these integers have been measured in 1D bosonic systems [15,25,26], the 2D bosonic case has been limited to atomics lattices [7].Here, we experimentally demonstrate that selective manipulation of the edge can be exploited to measure topological invariants, i.e., the winding number of the edge states. We implement an integer quantum Hall system using a fixed, uniform synthetic gauge field in the bulk and couple an additional tunable gauge field only to the edge. The edge state energy spectra flows as a function of this tunable flux. With insertion of a unit quantum of flux, the edge state resonances move by ±1, which is the winding number of edge states in our system. This spectral flow can be directly observed in an experiment as the flow of transmission resonances, and thus provides a direct measurement of the winding number of edge states. For this demonstration, we employ the unique ability of our photonic system to selectively manipulate edge states -a feature that is challenging to achieve in current electronic and atomic systems.To model the spectral flow of a quantum Hall edge, with winding number k = 1, we consider a linear edge dispersion E p = vp where E p is the energy, v is the group velocity, and p is the momentum along the edge. When a gauge flux (θ) is coupled to the edge, the momentum is replaced by the covariant momentum, i.e.,where L is the length of the edge and q is the charge of the edge excitations. For non-interacting photons, the charge q = 1. Note that the corre...

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, and the nontrivial topology is a result of next-nearest couplings with nonzero staggered phases. The system exhibits a topological phase transition between trivial and spin Chern insulator phases when the sublattices are frequency detuned. Such topological phase transitions can be easily induced by thermal or electro-optic modulators, or nonlinear cross phase modulation. We use this lattice to design reconfigurable topological waveguides, with potential applications in on-chip photon routing and switching.

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We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a twodimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically non-trivial bandgap. Using direct imaging and on-chip transmission measurements, we show that the bandgap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counter-clockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. We show that the two pseudospins acquire opposite hopping phases and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing.Photonics has emerged as a versatile platform to explore model systems with nontrivial band topology, a phenomenon originally associated with condensed matter systems [1,2]. For example, photonic systems have realized analogues of the integer quantum Hall effect [3][4][5][6][7], Floquet topological insulators [8][9][10][11], quantum spin-Hall and valley-Hall phases [12][13][14][15][16], as well as topological crystalline insulators [17][18][19]. From an application perspective, the inherent robustness of the topological systems has enabled the realization of photonic devices that are protected against disorder, such as optical delay lines [6,7], lasers [20][21][22], quantum light sources [23], and quantum-optic interfaces for light-matter interactions [18]. At the same time, features unique to bosonic systems, such as the possibility of introducing gain and loss into the system [24-28], parametric driving, and squeezing of light [23,29,30], have provided an opportunity to explore topological phases that cannot be realized in fermionic systems.Despite these advances, there has not yet been a nanophotonic realization of the anomalous quantum Hall phase -a two-dimensional Chern insulator with zero net gauge flux [31,32]. This is noteworthy because the various topological phases differ significantly in the origin of non-trivial band topology, and therefore offer different forms of topological protection. For instance, topological edge states in valley-Hall and topological crystalline insulator lattices manifest on internal boundaries between "opposite" domains instead of external edges [14,17], and are protected only against certain boundary deformations (e.g., 120 • bends but not 90 • bends) [14,17]. The quantum Hall and anomalous quantum Hall phases, by contrast, are significantly more robust: topological edge states can appear along external edges, and are protected irrespective of the lattice shape. Moreover, whereas the quantum Hal...