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Grigorenko I, Garcia ME, Bennemann KH. Theory for the optimal control of time-averaged quantities in quantum systems. Phys Rev Lett. 2002;89(23):233003doi: 10.1103/PhysRevLett.89.233003.
Grigorenko, I., Garcia, M. E., & Bennemann, K. H. (2002). Theory for the optimal control of time-averaged quantities in quantum systems. Physical review letters, 89(23), 233003. https://doi.org/10.1103/PhysRevLett.89.233003
Grigorenko, Ilia, et al. "Theory for the optimal control of time-averaged quantities in quantum systems." Physical review letters vol. 89,23 (2002): 233003. doi: https://doi.org/10.1103/PhysRevLett.89.233003
Grigorenko I, Garcia ME, Bennemann KH. Theory for the optimal control of time-averaged quantities in quantum systems. Phys Rev Lett. 2002 Dec 02;89(23):233003. doi: 10.1103/PhysRevLett.89.233003. Epub 2002 Nov 18. PMID: 12485004.
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Phys Rev Lett. 2002 Dec 02;89(23):233003. doi: 10.1103/PhysRevLett.89.233003. Epub 2002 Nov 18.

Theory for the optimal control of time-averaged quantities in quantum systems.

Physical review letters

Ilia Grigorenko, Martin E Garcia, K H Bennemann

Affiliations

  1. Institut für Theoretische Physik der Freien Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.

PMID: 12485004 DOI: 10.1103/PhysRevLett.89.233003

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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