Analytical theory for optimal control of multiphoton transitions

Abstract

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.