Chiral Quantum Transport with Perfect Circulation: From Floquet Engineering toAnyonic Dynamics

TL;DR

This paper establishes the fundamental physical conditions for perfect chiral quantum circulation, demonstrating their applicability across various platforms through Floquet engineering and anyon dynamics.

Contribution

It proves that translational invariance and an equidistant spectrum are necessary and sufficient for perfect chiral circulation, providing a unified criterion and explicit Hamiltonian.

Findings

Discrete translational invariance and equidistant spectrum are key for perfect circulation.

Two realizations: Floquet engineering and anyon-Hubbard model.

Results applicable to superconducting circuits, cold atoms, and photonic systems.

Abstract

Perfect chiral circulation-the sequential transfer of a quantum state around a closed loop with unit fidelity-has been achieved in specific few-site systems, yet the universal physical conditions underlying this phenomenon remain unclear. We prove that discrete translational invariance and an equidistant energy spectrum together constitute the necessary and sufficient conditions for perfect chiral circulation. With this criterion established, an exact closed-form Hamiltonian valid for arbitrary $N$-site rings naturally follows. In the minimal three-site ring, we demonstrate two physically distinct realizations: Floquet engineering of a driven open chain that restores translational invariance by equalizing the couplings, and correlated doublon dynamics in an anyon-Hubbard model where fractional statistics intrinsically provide the chiral flux that renders the spectrum equidistant. Our results establish unified physical criteria for perfect chiral circulation and demonstrate their applicability across diverse platforms such as superconducting circuits, cold atoms, classical electrical circuits, and photonic synthetic dimensions.