Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
- URL: http://arxiv.org/abs/2303.15359v1
- Date: Mon, 27 Mar 2023 16:31:17 GMT
- Title: Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
- Authors: Jing-jun Zhu, Kaipeng Liu, Xi Chen and St\'ephane Gu\'erin
- Abstract summary: 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.
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.
- Score: 3.8580539160777625
- License: http://creativecommons.org/licenses/by/4.0/
- 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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