Enhanced quantum sensing with multi-level structures of trapped ions

We present a method of enhanced sensing of 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, hence robustness to both external and controller noise is achieved. The scheme is applicable to either a single ion or an ensemble of ions. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the ⁴⁰ Ca ⁺ , ⁸⁸ Sr ⁺ and the ¹³⁸ Ba ⁺ ions. Taking experimental errors into account, we conclude that the coherence time of the robust qubit can be improved by up to ∼4 orders of magnitude compared to the coherence time of the bare states. We show how the robust qubit can be utilised for the task of sensing AC magnetic fields in the range ∼0.1 - 100 MHz with an improvement of ∼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 Be ⁺ , ²⁵ Mg ⁺ , ⁴³ Ca ⁺ , ⁸⁷ Sr ⁺ , ¹³⁷ Ba ⁺ , ¹¹¹ Cd ⁺ , ¹⁷¹ Yb ⁺ and the ¹⁹⁹ Hg ⁺ ions. This scheme enables the enhanced sensing of high-frequency fields at the GHz level.