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arXiv · 1508.03082

Time-optimal control fields for quantum systems with multiple avoided crossings

P. M. Poggi·F. C. Lombardo·D. A. Wisniacki
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Abstract

We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.

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P. M. Poggi, F. C. Lombardo, D. A. Wisniacki. 2015-08-12. Time-optimal control fields for quantum systems with multiple avoided crossings. https://doi.org/10.1103/physreva.92.053411

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