Escaping AB caging via Floquet engineering: photo-induced long-range interference in an all-band-flat model

Flat-band lattices hosting compact localized states are highly sensitive to external modulation, and the tailored design of a perturbation to imprint specific features becomes relevant. Here we show that periodic driving in the high-frequency regime transforms the all-flat-band diamond chain into one featuring two tunable quasi-flat bands and a residual flat band pinned at $E=0$. The interplay between lattice geometry and the symmetries of the driven system gives rise to drive-induced tunneling processes that redefine the interference conditions and open a controllable route to escaping Aharonov-Bohm caging. Under driving, the diamond chain effectively acquires the geometry of a dimerized lattice, exhibiting charge oscillations between opposite boundaries. This feature can be exploited to generate two-particle entanglement that is directly accessible experimentally. The resulting drive-engineered quasi-flat bands thus provide a versatile platform for manipulating quantum correlations, revealing a direct link between spectral fine structure and dynamical entanglement.

💡 Research Summary

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The paper investigates how a high‑frequency periodic drive can be used to engineer the band structure and dynamics of an all‑band‑flat (ABF) diamond chain that originally exhibits perfect Aharonov‑Bohm (AB) caging. In the static model a magnetic flux ϕ = π threads each plaquette, rendering all three energy bands completely flat (E = 0, ±2J) and forcing every eigenstate into a compact localized state (CLS). For a finite chain with an extra C‑site at each end, two pairs of edge modes appear at ±√2J, reflecting a square‑root topological invariant distinct from the usual SSH edge states.

The authors introduce a time‑periodic on‑site modulation of the U and D sublattices in the form of a square wave with amplitude A and frequency ω. Two driving protocols are considered: symmetric (ζ = +1) where U and D are modulated in phase, and antisymmetric (ζ = −1) where they are out of phase. The total Hamiltonian is (H_{\text{tot}}(k,t)=H_0(k)+H_d(t)).

Using Floquet theory in the high‑frequency regime (ω > 2J), they perform a Magnus/van Vleck expansion. The zeroth‑order effective Hamiltonian simply renormalizes the nearest‑neighbour hopping J by the Bessel factor (J_0(\tilde A)) with (\tilde A=A/ω). For symmetric driving all three bands remain exactly flat, merely shifted in energy. In contrast, antisymmetric driving introduces a complex phase on the C↔D hopping, and the second‑order term (∝ J³ (\tilde A)/ω²) generates long‑range hoppings (next‑nearest and second‑nearest neighbours). These photon‑assisted processes break the perfect destructive interference that underlies AB caging, giving the upper and lower bands a small but controllable dispersion – the so‑called quasi‑flat bands.

Numerical quasienergy spectra confirm these analytical predictions: with ζ = −1 the bandwidth grows as ω is lowered, while ζ = +1 retains perfect flatness. The drive does not alter the net π‑flux per plaquette, so the chiral symmetry of the Floquet spectrum (E↔−E) is preserved via a dynamical chiral operator satisfying (\Gamma H_{\text{tot}}(k,t)\Gamma = -H_{\text{tot}}(k,-t)). Consequently, the edge states remain pinned at ±√2J and are robust against the drive.

Dynamically, the emergence of quasi‑flat bands allows wave packets initially localized in a CLS to leak out of the AB cage and perform coherent charge oscillations between opposite boundaries. This behavior mimics a dimerized Su‑Schrieffer‑Heeger (SSH) lattice that the driven diamond chain effectively becomes. The authors exploit this coherent tunnelling to propose a protocol for generating two‑particle entanglement: starting from a product state with particles localized at opposite ends, the drive induces Rabi‑like oscillations between the flat and quasi‑flat bands, leading to periodic entanglement entropy oscillations with a non‑zero time‑averaged value. The entanglement generation relies on the photo‑induced long‑range hoppings and can be detected via standard correlation measurements in ultracold‑atom, photonic‑waveguide, or superconducting‑circuit platforms.

The paper also discusses symmetry aspects: static on‑site potentials break chiral symmetry, but the time‑periodic square wave restores an effective chiral symmetry in the Floquet picture, protecting the edge modes. The high‑frequency expansion converges for realistic parameters, though the second‑order coefficient involves an infinite series over photon‑harmonics that must be evaluated numerically.

In summary, the work demonstrates that Floquet engineering provides a controllable route to “escape” AB caging by introducing drive‑dependent long‑range hoppings, thereby converting an all‑flat‑band system into one with tunable quasi‑flat bands. This transformation enables coherent charge transport across the lattice and offers a practical method for dynamically generating and stabilizing entangled states, linking spectral fine structure directly to quantum correlations. The results open new avenues for designing driven flat‑band platforms for quantum simulation, topological quantum information processing, and engineered many‑body phases.