  The Berry phase of Bloch states can have profound effects on electron
dynamics lead to novel transport phenomena, such as the anomalous Hall effect
and the valley Hall effect. Recently, it was predicted that the Berry phase
effect can also modify the exciton states in transition metal dichalcogenide
monolayers, and lift the energy degeneracy of exciton states with opposite
angular momentum through an effective valley-orbital coupling. Here, we report
the first observation and control of the Berry-phase induced splitting of the
2p-exciton states in monolayer molybdenum diselenide using the intraexciton
optical Stark spectroscopy. We observe the time-reversal-symmetric analog of
the orbital Zeeman effect resulting from the valley-dependent Berry phase,
which leads to energy difference of +14 (-14) meV between the $2p^+$ and $2p^-$
exciton states in +K (-K) valley, consistent with the ordering from our ab
initio GW-BSE results. In addition, we show that the light-matter coupling
between intraexciton states are remarkably strong, leading to prominent
valley-dependent Autler-Townes doublet under resonant driving. Our study opens
up new pathways to coherently manipulate the quantum states and excitonic
excitation with infrared radiation in two-dimensional semiconductors.
