  The development of Quantum Simulators, artificial platforms where the
predictions of many-body theories of correlated quantum materials can be tested
in a controllable and tunable way, is one of the main challenges of condensed
matter physics. Here we introduce artificial lattices made of lead halide
perovskite nanocubes as a new platform to simulate and investigate the physics
of correlated quantum materials. The ultrafast optical injection of quantum
confined excitons plays the role of doping in real materials. We show that, at
large photo-doping, the exciton gas undergoes an excitonic Mott transition,
which fully realizes the magnetic-field-driven insulator-to-metal transition
described by the Hubbard model. At lower photo-doping, the long-range
interactions drive the formation of a collective superradiant state, in which
the phases of the excitons generated in each single perovskite nanocube are
coherently locked. Our results demonstrate that time-resolved experiments span
a parameter region of the Hubbard model in which long-range and phase-coherent
orders emerge out of a doped Mott insulating phase. This physics is relevant
for a broad class of phenomena, such as superconductivity and charge-density
waves in correlated materials whose properties are captured by doped Hubbard
models.
