[Paper Review] Protecting Quantum Superposition and Entanglement with Photonic Higher-Order Topological Crystalline Insulator

Yao Wang, Biye Xie+11 more|arXiv (Cornell University)|Jun 14, 2020

Topological Materials and Phenomena4 references4 citations

TL;DR

This paper demonstrates experimentally that photonic higher-order topological crystalline insulators, fabricated via femtosecond laser direct writing, protect single-photon quantum superposition and entangled photon states from diffusion-induced decoherence. By engineering $C_4$ and $C_2$ symmetric lattices and using single-photon imaging, the study reveals topologically protected corner states that preserve quantum coherence, establishing a robust mechanism for topological protection in quantum information systems.

ABSTRACT

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime.

Motivation & Objective

• To investigate the role of higher-order topological crystalline insulators in protecting quantum superposition and entanglement in photonic lattices.
• To experimentally realize and characterize topological corner states in two-dimensional photonic lattices with $C_4$ and $C_2$ symmetry.
• To demonstrate the robustness of quantum states against decoherence induced by diffusion in a topologically protected framework.
• To establish a direct link between topological invariants, crystalline symmetry, and quantum coherence in photonic quantum systems.

Proposed method

• Femtosecond laser direct writing was used to fabricate 2D photonic waveguide lattices with $8\times8$ sites, enabling precise control over lattice geometry and topological properties.
• Single-photon injection was performed via superposition states to probe the dynamics of quantum superposition across the lattice.
• Photon distribution and return probability were measured using heralded single-photon imaging techniques to map the evolution of quantum states.
• Theoretical modeling based on a tight-binding Hamiltonian with asymmetric couplings was used to describe the system, with topological invariants derived from the filling anomaly and symmetry protection.
• Symmetry analysis was performed to distinguish between $C_4$ and $C_2$ topological phases, revealing differences in corner state degeneracy and topological invariants.
• Non-Hermitian perturbations were introduced to test robustness, showing that corner states remain topologically protected with nearly real energies even under small non-Hermitian on-site potentials.

Experimental results

Research questions

• RQ1 Can photonic higher-order topological crystalline insulators protect single-photon superposition states from diffusion-induced decoherence?
• RQ2 How does the crystalline symmetry ($C_4$ vs $C_2$) influence the formation and topological protection of corner states in photonic lattices?
• RQ3 To what extent do topological corner states preserve quantum entanglement in multi-partite photonic systems?
• RQ4 What is the role of chiral symmetry and bulk polarization in stabilizing topologically protected zero-dimensional states in photonic lattices?
• RQ5 How does the topological protection in this system compare to that in quadrupolar insulators or all-dielectric photonic crystals?

Key findings

• The experimentally observed corner states in $C_4$-symmetric lattices are non-degenerate and preserve the relative phase of the initial superposition state, enabling photon distribution across multiple corners over evolution.
• In $C_2$-symmetric lattices, the corner states remain topologically protected and exhibit distinct topological invariants compared to $C_4$-symmetric systems, confirming symmetry-dependent topological phases.
• The return probability to the initial corner state remains high over 30 mm of propagation, indicating strong robustness against disorder and diffusion.
• Entangled photon states injected into the lattice maintain their quantum correlations, demonstrating topological protection of multi-partite entanglement.
• The corner states behave as bound states in the continuum (BIC) and remain isolated from bulk and edge states under small perturbations, confirming topological protection via chiral and $C_4$/$C_2$ symmetries.
• Non-Hermitian on-site potentials do not localize the corner states, as their energies remain nearly real and exponentially stable with increasing system size, confirming topological robustness.