Impurity in a bosonic Josephson junction: Swallowtail loops, chaos, self-trapping, and Dicke model

We study a model describing N identical bosonic atoms trapped in a double-well potential together with a single-impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the …