  Two dimensional lattices are an important stage for studying many aspects of
quantum physics, in particular the topological phases. The valley Hall and
anomalous Hall effects are two representative topological phenomena. Here we
show that they can be unified in a strained honeycomb lattice, where the
hopping strengths between neighboring sites are designed by mimicking those
between the Fock states in a three-mode Jaynes-Cummings model. Such a strain
induces an effective magnetic field which results in quantized Landau levels.
The eigenstates in the zeroth Landau level can be represented by the
eigenstates of a large pseudo-spin. We find that the valley Hall current and
the chiral edge current in the Haldane model correspond to the spin precession
around different axes. Our study sheds light on connection between seemingly
unrelated topological phases in condensed matter physics.
