Theory for the optimal control of time-averaged quantities in quantum systems |
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Authors: | Grigorenko Ilia Garcia Martin E Bennemann K H |
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Affiliation: | Institut für Theoretische Physik der Freien Universit?t Berlin, Arnimallee 14, 14195 Berlin, Germany. |
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Abstract: | We present a variational theory for the optimal control of quantum systems with relaxation over a finite time interval. In our approach, which is a nontrivial generalization of previous formulations and which contains them as limiting cases, the optimal control field fulfills a high-order Euler-Lagrange differential equation, which guarantees the uniqueness of the solution. We solve this equation numerically and also analytically for some limiting cases. The theory is applied to two-level quantum systems with relaxation, for which we determine quantitatively how relaxation effects limit the control of the system. |
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