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Nonequilibrium Landau-Zener Tunneling in Exciton-Polariton Condensates

For a coherent quantum mechanical two-level system driven with a linearly time-dependent detuning, the Landau-Zener model has served over decades as a textbook model of quantum dynamics. A particularly intriguing question is whether that framework can be extended to capture an intrinsical nonequilibrium nature for a quantum system with coherent and dissipative dynamics occurring on an equal footing. In this work, we are motivated to investigate the Landau-Zenner problem of polariton condensates in a periodic potential under nonresonant pumping, considering driven-dissipative Gross-Pitaevskii equations coupled to the rate equation of a reservoir. Using a two-mode approach, we find fluctuation of the reservoir can be considered as a constant and the relative phase plays a very important role. The evolution of the dissipative Landau-Zener model we obtain presents its adiabatic process very different from the closed system because the fluctuation of the reservoir has a peak and leads to the damping of the condensates. We substitute the fluctuation of the reservoir to Hamiltonian and get an effective two-level model. The motion of Hamiltonian in phase space is also discussed and is directly corresponding to the pumping rate. 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 when the pumping rate is far beyond the threshold.