Inhomogeneous Synthetic Fluxes in Optical Lattices

Synthetic gauge fields in optical lattices are usually engineered to realize a uniform magnetic flux. Here, we propose a scheme to generate spatially inhomogeneous fluxes and demonstrate how such fluxes reshape the single-particle spectrum. Within Wannier--Stark-assisted tunneling, onsite modulation produces a plaquette flux that depends on the orientation of the static tilt, whereas laser-assisted tunneling (LAT) does not. Using LAT, two coherent Raman processes with different momentum transfers imprint a dimerized Peierls phase that alternates the flux between neighboring plaquettes of a square lattice while keeping the mean flux fixed. A bond-selective Raman phase extends the scheme to the kagome lattice, where a parameter $ξ$ redistributes the flux between triangles and hexagons at fixed flux per unit cell. The Hofstadter--Rammal spectrum of the bipartite square lattice retains chiral symmetry for all $ξ$, whereas the kagome lattice lacks this symmetry, and its flux periodicity and reflection symmetries survive only at special values of $ξ$. As $ξ$ is reduced, the anomalous Landau levels of the kagome singular flat band are compressed toward the flat-band energy and evolve into a degenerate zero-energy manifold at $ξ=0$ with compactly localized states. The dynamical structure factor, accessible through Bragg scattering, resolves this evolution as a Rydberg-like series of peaks whose spectral span tracks the width of the anomalous-level tower and vanishes as $ξ\to0$. We discuss the frequency resolution and temperature required for its observation.