Phase-controlled transport of Floquet-driven compact chiral photonic states

Abstract

The Aharonov-Bohm (AB) effect remains a cornerstone of fundamental and applied physics. In this work, we utilize the AB caging effect originated from an effective magnetic field induced by multiorbital interactions, creating an all flat band (FB) lattice system. Normally, FB states are known for being compact in space and having a zero tail; therefore, their mobility in a linear environment is generally understood as impossible. We propose a Floquet driving protocol in an all-FB photonic system to fully control the dynamics of localized photonic states. The modulation of the Hamiltonian along the propagation coordinate allows the translation of compact states in the direction of constructive interference, resulting in an effective stroboscopic quantum walk-like effect. We find that the traveling states exist in chiral pairs. We experimentally implement the Floquet driven protocol using femtosecond laser written photonic waveguides and demonstrate directional control of the propagation, determined by the relative phase of the input condition.

The paper asks whether periodic driving can translate compact localized states through an otherwise Aharonov–Bohm-caged, all-flat-band photonic lattice, with direction controlled by the input phase. It studies a diamond waveguide array whose fundamental and higher-order modes generate positive and negative hoppings, producing an effective $\pi$ flux. The protocol alternates two static configurations, each with flat-band eigenvalues $0,\pm2t$, by exchanging the central waveguides’ mode types after propagation length $Z_\pi=\pi/(2t)$. Tight-binding and Floquet calculations predict compact, dispersionless translation: equal-amplitude, in-phase and out-of-phase two-site inputs move in opposite directions. The full-period quasienergy spectrum contains a flat band and oppositely sloped linear bands. A symmetry analysis identifies counterpropagating inputs as chiral partners. The undimerized system is gapless, however, so the reported winding calculations do not establish a globally defined band-resolved topological invariant. Experiments use femtosecond-written waveguides in 70-mm glass samples at 640 nm, with $Z_\pi=16.1$ mm and up to four concatenated segments. Output images show phase-dependent opposite transport, with mean displacement approximately one lattice spacing per segment, averaged over six input positions. A participation-ratio-based leakage indicator is around 3% through three segments and around 7% after four; this is not a direct leaked-power measurement. The stated experimental limitations are fabrication asymmetries, unbalanced couplings, incomplete transfers and accumulating errors. Longer propagation may introduce further-neighbor coupling that compromises chiral symmetry and compact transport. Abrupt mode-type changes can also cause loss or imperfect conversion if the central sites are occupied during switching.