Fast quantum driving in two-level systems with interaction and nonlinear sweep

We investigate high-fidelity fast quantum driving in a generalized nonlinear two-level system with both interparticle interaction and nonlinear energy sweep. We find that fast quantum dynamics depend on the interaction, energy sweep parameter, and energy sweep strength. We show that the driving protocol for a large energy sweep parameter reaches a given final high fidelity in a shorter time. The interparticle interaction can influence the quantum driving dynamics and can even break the quantum speed limit of the linear model. For the attractive interaction, the minimal time decreases monotonically as energy sweep strength increases, while it increases for the repulsive interaction. We also study a critical behavior and obtain analytical expressions of a critical interaction or a critical sweep strength, beyond which the target state cannot be achieved with high fidelity.