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 . 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.
1. Physical Review Letters 81, 5888 (1998)
2. Optics Letters 39, 5892 (2014)
Periodic arrays of evanescently coupled optical waveguides – known as photonic lattices – are a powerful experimental platform for exploring a range of semi-classical and quantum phenomena including topological phases of matter. In these artificial crystals of optical waveguides, the dynamics of a single-particle wavefunction can be experimentally emulated by probing the evolution of optical fields along the propagation distance . In many photonic lattice simulators, unlike fiber networks, the effective time-evolution of a specific input state is measured over relatively short timescales, which is set by the maximum propagation distance of the fabricated lattice, and hence, accessing long “time” dynamics constitutes a severe experimental challenge. In this work, we overcome this limitation by placing the photonic lattice inside a (linear or ring) cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon avalanche detector array , offers quasi-real time-resolved measurements after each round trip. We apply the state-recycling and time-resolved detection techniques to ultrafast-laser-fabricated photonic lattices emulating Dirac fermions and anomalous Floquet topological phases . We also show how this new platform allows realizing synthetic pulsed electric fields, which can be used to drive transport within photonic lattices. This work opens a new route towards the long-time-detection of the analogous wavefunction in engineered photonic lattices and the realization of hybrid analog-digital simulators.
1. Nature 424, 817 (2003)
2. Custom Integrated Circuits Conference, CICC’09. IEEE, 77–80 (2009)
In this paper we report the fabrication and mid-infrared characterization (λ = 3.39 μm) of evanescent field directional couplers. These devices were fabricated using the femtosecond laser direct-writing technique in commercially available Gallium Lanthanum Sulphide (GLS) glass substrates. We demonstrate that the power splitting ratios of the devices can be controlled by adjusting the length of the interaction section between the waveguides, and consequently we demonstrate power splitting ratios of between 8% and 99% for 3.39 μm light. We anticipate that mid-IR beam integrated-optic beam combination instruments based on this technology will be key for future mid-infrared astronomical interferometry, particularly for nulling interferometry and earth-like exoplanet imaging.