Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States
Abstract
We introduce the temporal quadrupole moment and leverage its nonreciprocal frequency-converting topological corner states to experimentally realize a magnet-free transceiving circulator in a topological time-modulated microwave metasurface. Under periodic driving, the temporal quadrupole moment evolves the corner charge of a bulk-gapped lattice over the drive cycle, generating two distinct families of topologically protected corner states: a corner mode at quasienergy ε=0 and a purely dynamical period-doubled mode at ε=π/T that exists only under periodic driving. We show that the relative phase between the two time-modulated coupling channels that generate it acts as a synthetic gauge field, breaking time-reversal symmetry while leaving the corner-mode topological protection intact. Specifically, a signal launched into the metasurface at TX port at frequency is up-converted and radiated into free space, while a free-space wave at is preferentially captured and routed --- at the same frequency, unconverted --- to RX port rather than back to TX port; the reverse itinerary is forbidden by the same broken symmetry. We confirm the temporal quadrupole moment, its associated Floquet corner states, and the resulting nonreciprocal frequency conversion through spatial field-intensity and angle-resolved radiation measurements of the time-modulated array on a fabricated microwave prototype.
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BibTeX
@misc{taravati2026temporal,
title = {{Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States}},
author = {Sajjad Taravati and Jingbang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23384},
eprint = {2609.23384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23384},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States
AU - Sajjad Taravati
AU - Jingbang Liu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.23384
UR - https://arxiv.org/abs/2609.23384
AB - We introduce the temporal quadrupole moment and leverage its nonreciprocal frequency-converting topological corner states to experimentally realize a magnet-free transceiving circulator in a topological time-modulated microwave metasurface. Under periodic driving, the temporal quadrupole moment evolves the corner charge of a bulk-gapped lattice over the drive cycle, generating two distinct families of topologically protected corner states: a corner mode at quasienergy ε=0 and a purely dynamical period-doubled mode at ε=π/T that exists only under periodic driving. We show that the relative phase between the two time-modulated coupling channels that generate it acts as a synthetic gauge field, breaking time-reversal symmetry while leaving the corner-mode topological protection intact. Specifically, a signal launched into the metasurface at TX port at frequency is up-converted and radiated into free space, while a free-space wave at is preferentially captured and routed --- at the same frequency, unconverted --- to RX port rather than back to TX port; the reverse itinerary is forbidden by the same broken symmetry. We confirm the temporal quadrupole moment, its associated Floquet corner states, and the resulting nonreciprocal frequency conversion through spatial field-intensity and angle-resolved radiation measurements of the time-modulated array on a fabricated microwave prototype.
ER -