Modulated pulses compensating classical noise

TL;DR

This paper develops finite-duration pulse corrections for classical noise in quantum control, designing amplitude and frequency modulated pulses that effectively mitigate decoherence effects up to second or third order.

Contribution

It introduces a systematic method to design modulated pulses that compensate classical noise effects in quantum systems up to third order in pulse duration.

Findings

Designed b0 and b0/2 pulses with amplitude and frequency modulation.

Developed low-amplitude replacement for XY8 cycles.

Classical noise pulses are weaker and simpler than quantum noise pulses.

Abstract

We consider pulses of finite duration for coherent control in the presence of classical noise. We derive the corrections to ideal, instantaneous pulses for the case of general decoherence (spin-spin relaxation and spin-lattice relaxation) up to and including the third order in the duration \tau_p of the pulses. For pure dephasing (spin-spin relaxation only), we design \pi and \pi/2 pulses with amplitude and/or frequency modulation which resemble the ideal ones up to and including the second order in \tau_p. For completely general decoherence including spin-lattice relaxation the corrections are computed up to and including the second order in \tau_p as well. Frequency modulated pulses are determined which resemble the ideal ones. They are used to design a low-amplitude replacement for XY8 cycles. In comparison with pulses designed to compensate quantum noise less conditions have to be fulfilled. Consequently, we find that the classical pulses can be weaker and simpler than the corresponding pulses in the quantum case.