Optimization of short coherent control pulses

Abstract

Experimentally, however, this idealized situation is not realistic. The real pulses are always of finite amplitude and of finite length. So the question must be addressed which effect a finite pulse duration p has. We want to elucidate this issue in the present work theoretically in a fully quantum mechanical framework. The issue of pulses of finite duration and finite amplitude has been considered in other papers. Viola and Knill generalized their previous approach of averaging over a symmetry group 16 by instantaneous changes of the effective Hamiltonian to continuous changes requiring only finite, bounded control amplitudes 17. But the presence of the coupling to the bath during the pulses has not been considered. Khodjasteh and Lidar considered the effect of finite pulse duration in a comprehensive comparison of various schemes for pulse sequences 18. They did not consider to make the detrimental effects of the finite pulse duration vanish on the level of the individual pulse, but they discussed possible cancellations on the higher hierarchical level of the pulse sequence. In the present work, we will choose another route and aim at reducing the decoherence due to finite pulse duration already on the level of the single pulse. As a side remark, we note that the statement in Ref. 18 on optimized pulse sequences 8 that they hold only for bosonic bath operators is very likely not to be correct. It has been conjectured very recently by Lee et al. 19 that the optimized sequences apply to the most general phase decoherence model.