Tuning the Order of the Nonequilibrium Quantum Phase Transition in a Hybrid Atom-Optomechanical System*

A quantum many-body hybrid system is considered formed by a nanomembrane, which interacts optomechanically with light in a pumped cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. An effective atom-membrane coupling can be realized in two different ways: first, the membrane is coupled to the motion of the atoms in the lattice$^1$ and, second, the motion of the membrane is coupled to transitions between two internal atomic states$^2$. By tuning the applied laser intensity, the optomechanical coupling of the membrane motion to the atomic motional or internal states can be tuned and a nonequilibrium quantum phase transition occurs above a critical intensity. Focussing on the latter case, the nonequilibrium quantum phase transition is characterized by a sizeable occupation of the energetically higher internal states and a displaced membrane. In contrast to the motional coupling scheme, its order can be changed by tuning the transition frequency.\\ ~$^1$ N. Mann, M. Reza Bakhtiari, A. Pelster, M. Thorwart, Phys. Rev. Lett. \textbf{120}, 063605 (2018)\\ ~$^2$ N. Mann, A. Pelster, M. Thorwart, submitted (arXiv:1810.12846)