Abstract
First order phase transitions are ubiquitous in nature, however, this notion is ambiguous and highly debated in the case of quantum systems out of thermal equilibrium. We construct a paradigmatic example which allows for elucidating the key concepts. We show that atoms in an optical cavity can manifest a first-order dissipative phase transition where the stable co-existing phases are quantum states with high quantum purity. These states include hyperfine ground states of atoms and coherent states of electromagnetic field modes. The scheme benefits from the collective enhancement of the coupling between the atoms and the cavity field. Thereby we propose a readily feasible experimental scheme to study the dissipative phase transition phenomenology in the quantum limit, allowing for, in particular, performing a finite-size scaling to the thermodynamic limit.