  Quantum simulation is a promising approach to understand complex strongly
correlated many-body systems using relatively simple and tractable systems.
Photon-based quantum simulators have great advantages due to the possibility of
direct measurements of multi-particle correlations and ease of simulating
non-equilibrium physics. However, interparticle interaction in existing
photonic systems is often too weak limiting the potential of quantum
simulation. Here we propose an approach to enhance the interparticle
interaction using exciton-polaritons in MoS$_2$ monolayer quantum-dots embedded
in 2D photonic crystal microcavities. Realistic calculation yields optimal
repulsive interaction in the range of $1$-$10$~meV --- more than an order of
magnitude greater than the state-of-art value. Such strong repulsive
interaction is found to emerge neither in the photon-blockade regime for small
quantum dot nor in the polariton-blockade regime for large quantum dot, but in
the crossover between the two regimes with a moderate quantum-dot radius around
20~nm. The optimal repulsive interaction is found to be largest in MoS$_2$
among commonly used optoelectronic materials. Quantum simulation of strongly
correlated many-body systems in a finite chain of coupled cavities and its
experimental signature are studied via exact diagonalization of the many-body
Hamiltonian. A method to simulate 1D superlattices for interacting
exciton-polariton gases in serially coupled cavities is also proposed.
Realistic considerations on experimental realizations reveal advantages of
transition metal dichalcogenide monolayer quantum-dots over conventional
semiconductor quantum-emitters.
