  We show that a hybrid atom-optomechanical quantum many-body system with two
internal atom states undergoes both first- and second-order nonequilibrium
quantum phase transitions. A nanomembrane is placed in a pumped optical cavity,
whose outcoupled light forms a lattice for an ultracold Bose gas. By changing
the pump strength, the effective membrane-atom coupling can be tuned. Above a
critical intensity, a symmetry-broken phase emerges which is characterized by a
sizeable occupation of the high-energy internal states and a displaced
membrane. The order of this nonequilibrium quantum phase transition can be
changed by tuning the transition frequency. For a symmetric coupling, the
transition is continuous below a certain transition frequency and discontinuous
above. For an asymmetric coupling, a first-order phase transition occurs.
