Ultrafast control

Alexander Nikolaevich Pechen, Nikolay Borisovich Ilin

Abstract In this work we study extrema of objective functionals for ultrafast manipulation by a qubit. Traps are extrema of the objective functionals which are optimal for manipulation by quantum systems only locally, not globally. Prior work has devoted a large amount of effort to the analysis of traps for quantum systems controlled by laser pulses which are long enough, and, for example, manipulation by a qubit with long control pulses was shown to be trap-free. Ultrafast femtosecond and attosecond control has now become widely applicable, which makes the analysis of traps on the ultrafast time scale a necessity. We complete such analysis for a qubit and show that ultrafast state transfer in a qubit remains trap-free for a wide range of the initial and final states of the qubit. We prove that for this range the probability of transition between the initial and the final states has a saddle but no traps.

Mikhail A. Noginov

Hugo E. L. Martay, David J. McCabe, Duncan G. England +3 more

Calculations relating to two experiments that demonstrate coherent control of preformed rubidium-85 molecules in a magneto-optical trap using ultrafast laser pulses are presented. The two experiments are a step toward the stabilization of ultracold rubidium dimers using ultrafast lasers. In the first experiment, it is shown that preassociated molecules in an incoherent mixture of states can be made to oscillate coherently using a single ultrafast pulse. A mechanism that can transfer molecular population to more deeply bound vibrational levels is used in the second. Optimal parameters of the control pulse are presented for the application of the mechanism to molecules in a magneto-optical trap. The calculations make use of an experimental determination of the initial state of molecules photoassociated by the trapping lasers in the magneto-optical trap and use shaped pulses consistent with a standard ultrafast laser system. The experiment's purpose is to demonstrate and evaluate the use of ultrafast shaped pulses to manipulate ultracold rubidium dimers with a view to the eventual stabilization of the molecules.

J. Stajic

Boris O Volkov, Oleg Vasilevich Morzhin, Alexander Nikolaevich Pechen

Abstract Mathematical analysis of quantum control landscapes, which aims to prove either absence or existence of traps for quantum control objective functionals, is an important topic in quantum control. In this work, we provide a rigorous analysis of quantum control landscapes for ultrafast generation of single-qubit quantum gates and show, combining analytical methods based on a sophisticated analysis of spectrum of the Hessian, and numerical optimization methods such as gradient ascent pulse engineering, differential evolution, and dual annealing, that control landscape for ultrafast generation of phase shift gates is free of traps.