Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States

Sajjad Taravati; Jingbang Liu

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arXiv · 2609.23384

Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States

Sajjad Taravati·Jingbang Liu

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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 $\varepsilon=0$ and a purely dynamical period-doubled mode at $\varepsilon=π/T$ 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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Sajjad Taravati, Jingbang Liu. 2026-09-20. Temporal Quadrupole Moments: Floquet Higher-Order Topology with Nonreciprocal Frequency-Converting Corner States. https://arxiv.org/abs/2609.23384

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