Analytical theory for optimal control of multiphoton transitions (6 pages)

Martin Weitz, Giovanni Cennini

Ilya Grigorenko, Martı́n E. Garcia

Using the Floquet formalism and the adiabatic approximation we develop a theory for optimal control of a multilevel quantum system interacting with an external electric field under multiphoton resonance conditions. Optimal solutions for the case of control over a time interval are presented. We derive a differential equation to determine the shape of the optimal pulse, and show how the order of the multiphoton resonance affects the solution. In particular, we demonstrate that optimal control in the case of two-photon resonance and using only adiabatically shaped control pulses represents a special degenerate case, for which the shape of the pulse cannot be optimized. Thus, for this particular case the final state of the controlled system is completely determined by the pulse energy.

Dewen Cao, Yaoxiong Wang, Shouzhi Li +3 more

Farhad H. M. Faisal

Toshiya Takami, Hiroshi Fujisaki

We examine random matrix systems driven by an external field in view of optimal control theory (OCT). By numerically solving OCT equations, we can show that there exists a smooth transition between two states called "moving bases" which are dynamically related to initial and final states. In our previous work [J. Phys. Soc. Jpn. 73, 3215 (2004); Adv. Chem. Phys. 130A, 435 (2005)], they were assumed to be orthogonal, but in this paper, we introduce orthogonal moving bases. We can construct a Rabi-oscillation-like representation of a wave packet using such moving bases, and derive an analytic optimal field as a solution of the OCT equations. We also numerically show that the newly obtained optimal field outperforms the previous one.

Farhad H. M. Faisal, A. Dalgarno