  In monolayer transition metal dichalcogenides time-reversal symmetry,
combined with space-inversion symmetry, defines the spin-valley degree of
freedom. As such, engineering and control of time-reversal symmetry by optical
or magnetic fields constitutes the foundation of valleytronics. Here, we
propose a new approach for the detection of broken time-reversal symmetry and
valley polarization in monolayer WSe$_2$ based on second harmonic generation.
Our method can selectively and simultaneously generate and detect a valley
polarization at the $\pm K$ valleys of transition metal dichalcogenides at room
temperature. Furthermore, it allows to measure the interference between the
real and imaginary parts of the intrinsic (electric dipole) and valley terms of
the second order nonlinear susceptibility. This work demonstrates the potential
and unique capabilities of nonlinear optics as a probe of broken time-reversal
symmetry and as a tool for ultrafast and non-destructive valleytronic
operations.
