Observation of a Localized Flat-Band State in a Photonic Lieb Lattice

Abstract

We demonstrate the first experimental realization of a dispersionless state, in a photonic Lieb lattice formed by an array of optical waveguides. This engineered lattice supports three energy bands, including a perfectly flat middle band with an infinite effective mass. We analyze, both experimentally and theoretically, the evolution of well-prepared flat-band states, and show their remarkable robustness, even in the presence of disorder. The realization of flat-band states in photonic lattices opens an exciting door towards quantum simulation of flat-band models in a highly controllable environment.

Bound states in the continuum

“…In some two-particle Hubbard models, there are bound states that can move into and out of the continuum continuously [235][236][237][238] ; the confinement requires no parameter tuning and has been credited to integrability 236 . Systems with a perfectly flat band can support localized states 239,240 . Localization can be induced with strong gain and/or loss, for example in a defect site with high loss 241 and in the bulk 200,202,242,243 or on the surface 244 of parity-time symmetric systems; ref.…”

Conical intersections for light and matter waves

“…Their vanishing group velocity and strong degeneracy can be directly observed via the existence of strongly localized yet propagation invariant (nondiffracting) wavepackets [51,52,56]. This nondiffracting behavior leads to a strong sensitivity to further perturbations such as disorder or interactions [45,47,73], analogous to slow light-enhanced nonlinear optical effects.…”

“…In this case, the prototypical example for studying the properties of integer pseudospin intersections has been the square-like "Lieb lattice" shown in Fig. 1(c), originally proposed for cold atoms [43,[45][46][47] and recently realized as a photonic lattice [48][49][50][51][52].…”

Nonlinear localized flat-band modes with spin-orbit coupling

“…Perturbations may hybridize CLSs with dispersive states through a spatially local resonant scenario [5], similar to Fano resonances [6]. The CLS existence has been experimentally probed in the same settings where FB lattices may be realized, as mentioned above: waveguiding arrays [7][8][9], exciton-polariton condensates [10], and atomic BECs [4]. The impact of various perturbations, such as disorder [5,11], correlated potentials [12,13], and external magnetic and electric fields [14], on FB lattices and the corresponding CLSs was studied too.…”