  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 Letter, we
show that the appearance of such a kink is a manifestation of a liquid-gas like
transition between two superfluids with different densities. The slopes in the
immediate neighborhood of the kink become divergent at the liquid-gas critical
points and display a critical scaling law with a critical exponent 1 in the
quantum critical region. Our predictions could be tested in current
experimental set-up.
