A first order superfluid-Mott insulator transition for a Bose–Hubbard model in an emergent lattice

The combination of strong correlation and emergent lattice can be achieved when quantum gases are confined in a superradiant Fabry–Perot cavity.In addition to the discoveries of exotic phases,such as density wave ordered Mott insulator and superfluid,a surprising kink structure is found in the slope of the cavity strength as a function of the pumping strength.In this article,we show that the appearance of such a kink is a manifestation of a liquid–vapour-like transition between two superfluids with different densities.The slopes in the immediate neighborhood of the kink become divergent at the liquid–vapour critical points and display a critical scaling law with a critical exponent 1 in the quantum critical region.