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Understanding the Hubbard model is crucial for investigating various quantummany-body states and its fermionic and bosonic versions have been largelyrealized separately. Recently, transition metal dichalcogenides heterobilayershave emerged as a promising platform for simulating the rich physics of theHubbard model. In this work, we explore the interplay between fermionic andbosonic populations, using a $\rm{WS}_2$/$\rm{WSe}_2$ heterobilayer device thathosts this hybrid particle density. We independently tune the fermionic andbosonic populations by electronic doping and optical injection of electron-holepairs, respectively. This enables us to form strongly interacting excitons thatare manifested in a large energy gap in the photoluminescence spectrum. Theincompressibility of excitons is further corroborated by measuring excitondiffusion, which remains constant upon increasing pumping intensity, as opposedto the expected behavior of a weakly interacting gas of bosons, suggesting theformation of a bosonic Mott insulator. We explain our observations using atwo-band model including phase space filling. Our system provides acontrollable approach to the exploration of quantum many-body effects in thegeneralized Bose-Fermi-Hubbard model.

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moir\'e $\rm{WS}_2$/$\rm{WSe}_2$ heterobilayer