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Register a new userDirect quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths
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Topological on-chip photonics based on tailored photonic crystals (PhC) that emulate quantum valley Hall effects has recently gained widespread interest due to its promise of robust unidirectional transport of classical and quantum information. We present a direct quantitative evaluation of topological photonic edge eigenstates and their transport properties in the telecom wavelength range using phase-resolved near-field optical microscopy. Experimentally visualizing the detailed sub-wavelength structure of these modes propagating along the interface between two topologically non-trivial mirror-symmetric lattices allows us to map their dispersion relation and differentiate between the contributions of several higher-order Bloch harmonics. Selective probing of forward and backward propagating modes as defined by their phase velocities enables a direct quantification of topological robustness. Studying near-field propagation in controlled defects allows to extract upper limits to topological protection in on-chip photonic systems in comparison to conventional PhC waveguides. We find that protected edge states are two orders of magnitude more robust as compared to conventional PhC waveguides. This direct experimental quantification of topological robustness comprises a crucial step towards the application of topologically protected guiding in integrated photonics, allowing for unprecedented error-free photonic quantum networks.
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The driven dissipative nonlinear multimode photonic dimer is considered as the simplest case of solitons in photonic lattices. It supports a variety of emergent nonlinear phenomena including gear soliton generation, symmetry breaking and soliton hopping. Surprisingly, it has been discovered that the accessibility of solitons in dimers drastically varies for the symmetric and anti-symmetric supermode families. Linear measurements reveal that the coupling between transverse modes, that give rise to avoided mode crossings, can be almost completely suppressed. We explain the origin of this phenomenon which we refer to as symmetry protection. We show its crucial influence on the dissipative Kerr soliton formation process in lattices of coupled high Q resonators of any type. Examining topologically protected states in the Su-Schrieffer-Heeger model of coupled resonators, we demonstrate that topological protection is not sufficient against the transversal mode crossing induced disorder. Finally, we show that the topological edge state can be symmetry protected by carefully choosing the balance between intra- and inter-resonator coupling to higher-order transverse modes, which suppresses mode crossings.
We use split-ring resonators to demonstrate topologically protected edge states in the Su-Schieffer-Heeger model experimentally, but in a slow-light wave with the group velocity down to $sim 0.1$ of light speed in free space. A meta-material formed by an array of complementary split-ring resonators with controllable hopping strength enables the direct observation in transmission and reflection of non-trivial topology eigenstates, including a negative phase velocity regime. By rotating the texture orientation of the diatomic resonators, we can explore all the band structures and unveil the onset of the trivial and non-trivial protected eigenmodes at GHz frequencies, even in the presence of non-negligible loss. Our system realizes a fully tunable and controllable artificial optical system to study the interplay between topology and slow-light towards applications in quantum technologies.
Topological spin liquids are robust quantum states of matter with long-range entanglement and possess many exotic properties such as the fractional statistics of the elementary excitations. Yet these states, short of local parameters like all topological states, are elusive for conventional experimental probes. In this work, we combine theoretical analysis and quantum Monte Carlo numerics on a frustrated spin model which hosts a $mathbb Z_2$ topological spin liquid ground state, and demonstrate that the presence of symmetry-protected gapless edge modes is a characteristic feature of the state, originating from the nontrivial symmetry fractionalization of the elementary excitations. Experimental observation of these modes on the edge would directly indicate the existence of the topological spin liquids in the bulk, analogous to the fact that the observation of Dirac edge states confirmed the existence of topological insulators.
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands, and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through explicit construction of microscopic models having robust $(d-2)$-dimensional edge states.
We experimentally demonstrate topological edge states arising from the valley-Hall effect in twodimensional honeycomb photonic lattices with broken inversion symmetry. We break inversion symmetry by detuning the refractive indices of the two honeycomb sublattices, giving rise to a boron nitride-like band structure. The edge states therefore exist along the domain walls between regions of opposite valley Chern numbers. We probe both the armchair and zig-zag domain walls and show that the former become gapped for any detuning, whereas the latter remain ungapped until a cutoff is reached. The valley-Hall effect provides a new mechanism for the realization of time-reversal invariant photonic topological insulators.
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