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

PABLO POGGI; FERNANDO LOMBARDO; D. A. WISNIACKI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2015 vol. 92 p. 1 - 10

1050-2947

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 the QSL time 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.