  Optical selection rule fundamentally determines the optical transition
between energy states in a variety of physical systems from hydrogen atoms to
bulk crystals such as GaAs. It is important for optoelectronic applications
such as lasers, energy-dispersive X-ray spectroscopy and quantum computation.
Recently, single layer transition metal dichalcogenide (TMDC) exhibits valleys
in momentum space with nontrivial Berry curvature and excitons with large
binding energy. However, it is unclear how the unique valley degree of freedom
combined with the strong excitonic effect influences the optical excitation.
Here we discover a new set of optical selection rules in monolayer WS2,imposed
by valley and exciton angular momentum. We experimentally demonstrated such a
principle for second harmonic generation (SHG) and two-photon luminescence
(TPL). Moreover, the two-photon induced valley populations yield net circular
polarized photoluminescence after a sub-ps interexciton relaxation (2p->1s) and
last for 8 ps. The discovery of this new optical selection rule in valleytronic
2D system not only largely extend information degrees but sets a foundation in
control of optical transitions that is crucial to valley optoeletronic device
applications such as 2D valley-polarized light emitting diodes (LED), optical
switches and coherent control for quantum computing.
