High Order Coherent Control Sequences of Finite-Width Pulses

TL;DR

This paper analyzes the effectiveness of high-order coherent control sequences of finite-width pulses in spin baths, showing that non-equidistant, adapted sequences outperform standard ones with lower energy costs.

Contribution

It introduces high-order control sequences that improve performance of finite-width pulses compared to ideal pulses, with optimized timing and energy efficiency.

Findings

Non-equidistant, adapted sequences outperform equidistant ones.

Sequences match ideal pulse performance up to A4^3 order.

Energy cost grows logarithmically with number of pulses.

Abstract

The performance of sequences of designed pulses of finite length $\tau$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(\tau^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.