Fig. 2.

Illustrating how level quantization and Landau–Zener (LZ) tunneling affect forced barrier crossing. (A) The four lowest instantaneous eigenvalues of a particle that is adiabatically driven by the harmonic trap from a periodic potential minimum to the nearest one. All avoided crossing gaps associated with LZ tunneling events encountered during the dynamics at times $t_1$, $t_2$, and $t_3$ are nonzero, even if invisible for $t_1$ and $t_2$ on this scale. The circle highlights the resonant tunneling described in text and represented in B. (B) A pictorial sketch of the tunneling event in which a particle in the ground level of the left well (0A) resonantly tunnels into the first excited level of the right well (1B).