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]

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...

We theoretically study the transport of time-bin entangled photon pairs in a two-dimensional topological photonic system of coupled ring resonators. This system implements the integer quantum Hall model using a synthetic gauge field and exhibits topologically robust edge states. We show that the transport through edge states preserves temporal correlations of entangled photons whereas bulk transport does not preserve these correlations and can lead to significant unwanted temporal bunching or anti-bunching of photons. We study the effect of disorder on the quantum transport properties; while the edge transport remains robust, bulk transport is very susceptible, and in the limit of strong disorder, bulk states become localized. We show that this localization is manifested as an enhanced bunching/anti-bunching of photons. This topologically robust transport of correlations through edge states could enable robust on-chip quantum communication channels and delay lines for information encoded in temporal correlations of photons.