Non-equilibrium $d-$ wave pair density wave order parameter in superconducting cuprates

We investigate the nonequilibrium pair density wave order parameter in a simple microscopic model with the ground state $d-$ wave spatially uniform superconductivity. After pushing the system out of equilibrium by a short-time induced order parameter, the system can exhibit robust free nondecaying oscillations of nonuniform superconducting order. In the weak nonequilibrium regime, the frequency of these oscillations is about $2\Delta/\hbar$ and the amplitude can be explained qualitatively by features of equilibrium free energy. In case when the system was taken far from equilibrium, it transits to a non-linear regime where even metastable coexistence of $d-$ wave superconducting and pair density wave gaps are possible.