We develop a general optimization framework for high-efficiency quantum cycles implemented with a trapped Bose-Einstein condensate, whose control parameters are the trap stiffness and the interaction strength, the latter tuned via Feshbach resonance. Combining a variational description of the condensate dynamics with Nelson's stochastic quantization, we map the quantum evolution onto an effective classical Ornstein-Uhlenbeck process, enabling the systematic optimization of each cycle stroke. The optimal protocol is obtained by minimizing a user-defined cost functional that selects the best trade-off between protocol duration and arbitrary physical constraints (such as the expended work or the proximity to an adiabatic evolution). The resulting protocols remain remarkably stable over repeated cycles, demonstrating the robustness of the optimization strategy. More generally, our framework provides a systematic route to the optimal control of nonlinear Schrödinger equations, with potential applications to quantum fluids, nonlinear optics, and quantum plasmas.

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• Quantum protocols
• Quantum fluids & solids
• Ultracold gases
• Schroedinger equation
• Stochastic differential equations