Photonic quadrupole topological phases

Abstract

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]

Higher-order topological solitonic insulators

“…Furthermore, the artifact effect of the corner states are also discussed in Supplementary Note 4. These findings echo the observations in photonic and phononic systems [13][14][15][16][17][18][19][20][21].…”

“…However, a higher-order, e.g., kth-order, topological insulator allows (n − k)-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index [5][6][7][8][9][10][11][12]. Interestingly, the experimental evidences of higher-order topological insulators (HO-TIs) were reported so far only in classical mechanical and electromagnetic metamaterials [13][14][15][16][17][18][19][20][21]. In terms of applications of HOTIs in spintronics, it is intriguing to ask if they can exist in magnetic system which is intrinsically, however nonlinear, in contrast to its phononic and photonic counterparts.…”

Higher‐Order Topological States in Surface‐Wave Photonic Crystals

“…After the submission of this work, we become aware of several independent works, which report on realization of higher‐order photonic topological states based on photonic crystals in a generalized Su‐Schrieffer‐Heeger model, or based on optical waveguide arrays in a breathing kagome lattice model, or realization of photonic topological quadrupole phases …”

Dynamics of two-dimensional topological quadrupole insulator and Chern insulator induced by real-space topological changes

“…The original proposal of the TQI 7 envisioned its realization in quantum simulators such as cold-atoms in optical potentials. Given the broad choices of quantum systems which may realize various TIs and HOTIs [10][11][12][13][14]16 , the dynamics analyzed in this work may be studied in systems allowing the formation of a cylinder or Mobius strip. For example, topological systems in a Mobius configuration have been demonstrated by using electronic circuits to simulate quantum particles in lattice potentials 32 .…”