LAUSR

For describing a coherent quantum two-level system driven by a linearly time-dependent energy separation of the diabatic states, the Landau-Zener model is routine to serve as a textbook model for its dynamics. Along this research line, a particularly intriguing question is whether the framework of Landau-Zener theory can be extended to an intrinsically nonequilibrium quantum system with coherent and dissipative dynamics occurring on an equal footing. In this work, we are motivated to investigate the Landau-Zener problem of polariton condensates in a periodic potential under nonresonant pumping by using the driven-dissipative Gross-Pitaevskii equations coupled to the rate equation. Within the two-mode approximation, a nonequilibrium Landau-Zener model, characterized by coherent and dissipative dynamics occurring on an equal footing, is derived. Fundamentally different from the previous Landau-Zener model, the total density of nonequilibrium Landau-Zener model, in general, is not the conserved quantity anymore due to the dissipative nature. In a surprise, the parameter regimes of the total density still being conserved can still be found. The motion of Hamiltonian of the nonequilibrium Landau-Zener problem in phase space is further discussed. The instability of the band structure can also be studied by the curvatures in phase space, and there may be two loops in the middle of the Brillouin zone. Detailed analysis of the nonequilibrium nature on the tunneling rate will open a new perspective toward understanding the Landau-Zener problem.