Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
Abstract
Using optimal control, we establish and link the ultimate bounds in time (referred to as quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete inversion, by using the Pontryagin maximum principle, we determine the optimal time, pulse area, or energy, for a given arbitrary accuracy. We show that the third-order Kerr terms can be absorbed in the detuning in order to lock the dynamics to the resonance. In the two-level problem, we determine the non-linear counterpart of the optimal -pulse inversion for a given accuracy. In the three-level problem, we obtain an intuitive pulse sequence similar to the linear counterpart but with different shapes. We prove the (slow) logarithmic increasing of the optimal time as a function of the accuracy.
Keywords
Cite
@article{arxiv.2303.15359,
title = {Optimal control and ultimate bounds of 1:2 nonlinear quantum systems},
author = {Jing-jun Zhu and Kaipeng Liu and Xi Chen and Stéphane Guérin},
journal= {arXiv preprint arXiv:2303.15359},
year = {2023}
}