Programmable Lattices for Non-Abelian Topological Photonics and Braiding

Area of Science:

• Quantum Physics
• Photonics
• Topological Matter

Background:

• Non-Abelian physics explores noncommutative operations and topological degrees of freedom.
• Reconfigurable non-Abelian platforms in photonics are crucial for testing quantum phenomena and harnessing topological complexity.

Purpose of the Study:

• To establish topological spinor lattices for non-Abelian programmable photonics.
• To design a building block for reconfigurable unitary coupling between pseudospin resonances.
• To emulate the extended quantum Hall family and engineer topologically protected edge states.

Main Methods:

• Designed a building block for reconfigurable unitary coupling between pseudospin resonances.
• Assembled building blocks into a lattice structure.
• Defined the braid group for pseudospin observables.

Main Results:

• Achieved a universal set of rotation gates through a coupling loop.
• Emulated the extended quantum Hall family.
• Revealed non-Abelian interface emergence in topologically trivial systems, enabling protected edge states.
• Demonstrated non-Abelian braiding and Yang-Baxter relations for pseudospin observables.

Conclusions:

• Established topological spinor lattices for non-Abelian programmable photonics.
• Enabled reconfigurable emulation of both Abelian and non-Abelian topological phenomena.
• Paved the way for novel topological quantum simulators and devices.