Pareto-optimality of pulses for robust population transfer in a ladder-type qutrit

Frequency-modulation schemes offer an alternative to standard Rabi pulses for realizing robust quantum operations. In this work, we investigate short-duration population transfer between the ground and first excited states of a ladder-type qutrit, with the goal of minimizing leakage into the second excited state. Our multiobjective approach seeks to reduce the maximum transient second-state population and maximize detuning robustness. Inspired by two-state models—such as the Allen-Eberly and Hioe-Carroll models—we extend these concepts to our system, exploring a range of pulse families, including those with super-Gaussian envelopes and polynomial detuning functions. We identify Pareto fronts for pulse models constructed from one of two envelope functions paired with one of four detuning functions. We then analyze how each Pareto-optimal pulse parameter influences the two Pareto objectives as well as amplitude robustness.