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We demonstrate the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in ultrafast-laser-fabricated photonic rhombic lattices. We engineer modulation-assisted tunneling processes that effectively produce complex-valued tunneling matrix elements leading to a non-zero magnetic flux per plaquette. In other words, the synthetic magnetic flux is generated by applying a strong linear detuning of the propagation constants along the lattice – in order to suppress the effective inter-site tunneling – and then by resonantly modulating the propagation constants with a required phase of modulation to restore and control the effective tunneling amplitudes. This synthetic magnetic field for light can be tuned by varying the phase of the modulation. When half a flux quantum is realized in each plaquette, all the energy bands collapse into non-dispersive (flat) bands and all eigenstates are completely localized in real space [1,2]. We demonstrate this magnetic flux induced localization phenomena, known as Aharonov-Bohm caging, by launching input states that overlap with the flat-band states and observing breathing motions of the optical intensity whose frequency is determined by the energy gaps in the spectrum [3]. Additionally, we explore the dynamics on the edge of the lattice and show how the corresponding edge-states can be continuously connected to the topological edge-states of a Creutz ladder. Our photonic lattice constitutes an appealing platform where the interplay between engineered gauge fields, frustration, localization and topological properties can be finely studied.
References:
1. Physical Review Letters 81, 5888 (1998)
2. Optics Letters 39, 5892 (2014)
3. arXiv:1805.03564
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