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We analyze the dynamics and final populations in a Landau-Zener problem for atwo level system (or qubit) when this system interacts with one harmonicoscillator mode that is initially set to a finite-temperature thermalequilibrium state. The harmonic oscillator could represent an external modethat is strongly coupled to the qubit, e.g. an ionic oscillation mode in amolecule, or it could represent a prototypical uncontrolled environment. Weanalyze the qubit's occupation probabilities at the final time in a number ofdifferent regimes, varying the qubit and oscillator frequencies, their couplingstrength and the temperature. In particular we find some surprisingnon-monotonic dependence on the coupling strength and temperature.

Landau-Zener transitions in a two-level system coupled to a finite-temperature harmonic oscillator