  Wigner crystals are prime candidates for the realization of regular electron
lattices under minimal requirements on external control and electronics.
However, several technical challenges have prevented their detailed
experimental investigation and applications to date. We propose an
implementation of two-dimensional electron lattices for quantum simulation of
Ising spin systems based on self-assembled Wigner crystals in transition-metal
dichalcogenides. We show that these semiconductors allow for minimally invasive
all-optical detection schemes of charge ordering and total spin. For incident
light with optimally chosen beam parameters and polarization, we predict a
strong dependence of the transmitted and reflected signals on the underlying
lattice periodicity, thus revealing the charge order inherent in Wigner
crystals. At the same time, the selection rules in transition-metal
dichalcogenides provide direct access to the spin degree of freedom via Faraday
rotation measurements.
