  We demonstrate inter-valley Bloch oscillation (BO) and Landau-Zener tunneling
(LZT) in an optically-induced honeycomb lattice with a refractive index
gradient. Unlike previously observed BO in a gapped square lattice, we show
non-adiabatic beam dynamics that are highly sensitive to the direction of the
index gradient and the choice of the Dirac cones. In particular, a
symmetry-preserving potential leads to nearly perfect LZT and coherent BO
between the inequivalent valleys, whereas a symmetry-breaking potential
generates asymmetric scattering, imperfect LZT, and valley-sensitive generation
of vortices mediated by a pseudospin imbalance. This clearly indicates that,
near the Dirac points, the transverse gradient does not always act as a simple
scalar force as commonly assumed, and the LZT probability is strongly affected
by the sublattice symmetry as analyzed from an effective Landau-Zener
Hamiltonian. Our results illustrate the anisotropic response of an otherwise
isotropic Dirac platform to real-space potentials acting as strong driving
fields, which may be useful for manipulation of pseudospin and valley degrees
of freedom in graphene-like systems.
