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Higher-order topological insulators in synthetic dimensions
Avik Dutt1, Momchil Minkov1, Ian A D Williamson1
1Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA.
Light, Science & Applications
|July 25, 2020
Summary
We introduce photonic higher-order topological insulators in synthetic dimensions, realizing protected corner modes. This work extends topological concepts to synthetic spaces, enabling novel phenomena beyond real-space limitations.
Area of Science:
- Condensed Matter Physics
- Photonics
- Quantum Physics
Background:
- Conventional topological insulators (TIs) exhibit boundary states protected by quantized bulk dipole moments.
- Higher-order topological insulators (HOTIs) feature topological states in lower dimensions, arising from quantized quadrupole or octupole moments.
- Existing HOTI research is limited to real-space dimensions.
Purpose of the Study:
- To construct and investigate photonic higher-order topological insulators (PHOTIs) in synthetic dimensions.
- To demonstrate the realization of topologically protected corner modes in a synthetic frequency dimension.
- To explore dynamical topological phase transitions and higher-order multipole moments in PHOTIs.
Main Methods:
- Construction of a quadrupole PHOTI using an array of modulated photonic molecules in a synthetic frequency dimension.
- Each photonic molecule consists of two coupled rings.
- Tuning the phase difference of modulation between adjacent coupled photonic molecules to induce phase transitions.
Main Results:
- Emergence of a quadrupole PHOTI with topologically protected corner modes.
- Observation of a dynamical topological phase transition by altering modulation phase differences.
- Demonstration of realizing higher-order multipole moments (e.g., hexadecapole) in synthetic dimensions.
- Creation of a 4D hypercubic synthetic lattice supporting 0D corner modes.
Conclusions:
- Synthetic dimensions provide a powerful platform for realizing higher-order topological phenomena.
- PHOTIs in synthetic dimensions overcome real-space limitations, enabling novel topological states.
- This approach opens avenues for exploring exotic topological phases and higher-order multipole moments beyond conventional systems.
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