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The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

We present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [1]. Grating assisted tunneling is inspired with laser assisted tunneling in ultracold atomic systems theoretically proposed in Refs. [2, 3], subsequently developed to experimentally realize Harper-Hofstadter Hamiltonian [4, 5]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We propose implementation of the Harper-Hofstadter Hamiltonian in these photonic lattices [1]. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k- space. We compare the light propagation in the realistic (continous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

photonic lattices, synthetic magnetic field, conical diffraction, Harper-Hofstadter Hamiltonian

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