Nonlinear Dicke Quantum Phase Transition and Its Quantum Witness in a Cavity-Bose–Einstein-Condensate System

We investigate nonlinear Dicke quantum phase transition (QPT) induced by inter-atomic nonlinear interaction and its quantum witness in a cavity-Bose–Einstein-condensate (BEC) system. It is shown that inter-atomic nonlinear interaction in a cavity BEC system can induce first-order Dicke QPT. It is found that this nonlinear Dicke QPT can happen in an arbitrary coupling regime of the cavity and atoms. It is demonstrated that the quantum speed limit time can witness the Dicke QPT through its sudden change at the critical point of the QPT.