# Enhanced quantum sensing with multi-level structures of trapped ions

## TL;DR

This paper introduces a robust qubit construction in trapped ions for enhanced AC magnetic field sensing, significantly improving coherence times and sensitivity, with practical implementations for various ion species and frequencies.

## Contribution

It presents a novel method to create robust qubits in trapped ions using continuous driving fields, leading to substantial improvements in magnetic field sensing performance.

## Key findings

- Coherence time improved by up to 4 orders of magnitude.
- Sensitivity to AC magnetic fields increased by approximately 2 orders of magnitude.
- Applicable to multiple ion species and frequency ranges, including GHz.

## Abstract

We present a method of sensing AC magnetic fields. The method is based on the construction of a robust qubit by the application of continuous driving fields. Specifically, magnetic noise and power fluctuations of the driving fields do not operate within the robust qubit subspace, and hence, robustness to both external and controller noise is achieved. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the $^{40}{\rm{Ca}}^{+}$, $^{88}{\rm{Sr}}^{+}$, and the $^{138}{\rm{Ba}}^{+}$ ions. Taking experimental errors into account, we conclude that the coherence time of the robust qubit can be improved by up to $\sim 4$ orders of magnitude compared to the coherence time of the bare states. We show how the robust qubit can be utilized for the task of sensing AC magnetic fields, leading to an improvement of $\sim 2$ orders of magnitude of the sensitivity. In addition, we present a microwave based sensing scheme that is suitable for ions with a hyperfine structure, such as the $^{9}{\rm{Be}}^{+}$,$^{25}{\rm{Mg}}^{+}$,$^{43}{\rm{Ca}}^{+}$,$^{87}{\rm{Sr}}^{+}$,$^{137}{\rm{Ba}}^{+}$,$^{111}{\rm{Cd}}^{+}$,$^{171}{\rm{Yb}}^{+}$, and the $^{199}{\rm{Hg}}^{+}$ ions. This scheme enables the enhanced sensing of high frequency fields at the GHz level.