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

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.

11 pages, 7 figures

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Cited by in corpus (6)

• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Superadiabatic driving of a three-level quantum system
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Optimal control of many-body quantum dynamics: chaos and complexity
• Manipulating matter waves in an optical superlattice