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Here, we present the application of a novel method for controlling thegeometry of a state-dependent honeycomb lattice: The energy offset between thetwo sublattices of the honeycomb structure can be adjusted by rotating theatomic quantization axis. This enables us to continuously tune between ahomogeneous graphene-like honeycomb lattice and a triangular lattice and toopen an energy gap at the characteristic Dirac points. We probe the symmetry ofthe lattice with microwave spectroscopy techniques and investigate the behaviorof atoms excited to the second energy band. We find a striking influence of theenergy gap at the Dirac cones onto the lifetimes of atoms in the excited band.

Breaking inversion symmetry in a state-dependent honeycomb lattice: Artificial graphene with tunable band gap