Probing Bulk Band Topology from Time Boundary Effect in Synthetic Dimension

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Wave Phenomena

Background:

• Temporal interfaces, arising from abrupt parameter changes, generate unique wave phenomena.
• Topological phases in materials are characterized by robust properties and bulk-boundary correspondence.
• Understanding wave behavior at dynamic interfaces is crucial for novel device applications.

Purpose of the Study:

• To investigate the topological characteristics of temporal interfaces.
• To establish a novel bulk-boundary correspondence for temporal interfaces.
• To demonstrate the use of temporal interfaces for probing topological phase transitions and invariants.

Main Methods:

• Analysis of incident waves at a temporal interface.
• Theoretical investigation of time-refracted and time-reflected waves.
• Demonstration in a synthetic frequency lattice with long-range couplings.

Main Results:

• Topological characteristics were identified at temporal interfaces separating distinct spatial topologies.
• A novel bulk-boundary correspondence for temporal interfaces was reported.
• The vanishing of time refraction or reflection was shown to indicate a topological phase transition.
• Bulk band topology differences predict nontrivial braiding in wave coefficients.

Conclusions:

• Temporal interfaces exhibit unique topological aspects.
• The time boundary effect can be utilized to probe topological phase transitions and invariants.
• Findings are robust against spatial boundary conditions and disorder, applicable to synthetic topological systems.