Control landscape for ultrafast manipulation by a qubit

TL;DR

This paper analyzes the control landscape for ultrafast qubit manipulation, demonstrating that ultrafast state transfer remains trap-free across a broad range of states, with only saddle points present.

Contribution

It provides a theoretical analysis showing the absence of traps in ultrafast qubit control landscapes, extending previous work from longer pulses to femtosecond and attosecond regimes.

Findings

Ultrafast state transfer in a qubit is trap-free for many initial and final states.

The transition probability landscape has saddle points but no traps.

The results support the feasibility of ultrafast quantum control without local optima.

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 but not globally. Much effort in prior works was devoted to the analysis of traps for quantum systems controlled by long enough laser pulses and, for example, manipulation by a qubit with long control pulses was shown to be trap-free. Ultrafast femtosecond and attosecond control becomes now widely applicable that motivates the necessity for the analysis of traps on the ultrafast time scale. We do 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 has no traps.