Cavity-assisted dynamical quantum phase transition at bifurcation points

Coupling a quantum many-body system to a cavity can create bifurcation points in its phase diagram, where the ground state makes sudden switchings between different phases. Here we study the dynamical quantum phase transition of a transverse field Ising model coupled to a cavity. We show that an infinitesimal quench of the cavity driving at the bifurcation points induces gradual evolution of the Ising model to pass across the quantum critical point and excites quasiparticles. Meanwhile, when the driving is slowly ramped through the bifurcation points, the adiabaticity of the evolution and the number of quasiparticle excitations are strongly affected by cavity-induced nonlinearity. Introducing and manipulating cavity-induced nonlinearity hence provide an effective approach to control the dynamics and the adiabaticity of adiabatic quantum processes. This model can be implemented with superconducting quantum circuits.