The evolutions of the probabilities p ± ( t ) (thick lines) in the instantaneous eigenstates of | φ ± 〉 and p e , g ( t ) (thin lines) in the bare states of | e , g 〉 . The horizonal dashed lines are the probabilities predicted by the Landau–Zener formula and the upper bound determined by Eq. (39). The parameters are λ 0 = 12 Hz , β = 0.3 Hz/s, and Ω 0 = 0.4 Hz .