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arXiv · 2303.15359

Optimal control and ultimate bounds of 1:2 nonlinear quantum systems

Jing-jun Zhu·Kaipeng Liu·Xi Chen·Stéphane Guérin
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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 $\pi$-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.

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Jing-jun Zhu, Kaipeng Liu, Xi Chen, Stéphane Guérin. 2023-03-27. Optimal control and ultimate bounds of 1:2 nonlinear quantum systems. https://doi.org/10.1103/physreva.108.042610

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