# Control methods for improved Fisher information with quantum sensing

## TL;DR

This paper interprets new quantum sensing methods that achieve a $T^4$ Fisher information scaling, explores pulse sequences to prolong this effect, and analyzes their relevance to experiments and finite coherence times.

## Contribution

It provides a new interpretation of the $T^4$ Fisher information scaling and proposes pulse sequences to extend this scaling in quantum sensing.

## Key findings

- Quadratic phase accumulation can be achieved with simple pulse sequences.
- Certain pulse sequences prolong the $T^4$ Fisher information scaling.
- The $T^3$ scaling is optimal for finite coherence times with multiple measurements.

## Abstract

Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the relative phase is accumulated quadratically with time, and show that this can be produced by a variety of simple pulse sequences. Interestingly, this scaling has a limited duration, and we show that certain pulse sequences prolong the effect. The performance of these schemes is analyzed and we examine their relevance to state-of-the-art experiments. We analyze the $T^{3}$ scaling of the Fisher information which appears when multiple synchronized measurements are performed, and is the optimal scaling in the case of a finite coherence time.