Diego Barberena

We propose protocols for the creation of useful entangled states in a system of spins collectively coupled to a bosonic mode, directly applicable to trapped-ion and cavity QED setups. The protocols use coherent manipulations of the spin-boson interactions naturally arising in these systems to prepare spin squeezed states exponentially fast in time. We demonstrate the robustness of the protocols by analyzing the effects of natural sources of decoherence in these systems and show their advantage compared to more standard slower approaches where entanglement is generated algebraically with time.

Developing the isolation and control of ultracold atomic systems to the level of single quanta has led to significant advances in quantum sensing, yet demonstrating a quantum advantage in real world applications by harnessing entanglement remains a core task. Here, we realize a many-body quantum-enhanced sensor to detect weak displacements and electric fields using a large crystal of $\sim 150$ trapped ions. The center of mass vibrational mode of the crystal serves as high-Q mechanical oscillator and the collective electronic spin as the measurement device. By entangling the oscillator and the collective spin before the displacement is applied and by controlling the coherent dynamics via a many-body echo we are able to utilize the delicate spin-motion entanglement to map the displacement into a spin rotation such that we avoid quantum back-action and cancel detrimental thermal noise. We report quantum enhanced sensitivity to displacements of $8.8 \pm 0.4~$dB below the standard quantum limit and a sensitivity for measuring electric fields of $240\pm10~\mathrm{nV}\mathrm{m}^{-1}$ in $1$ second ($240~\mathrm{nV}\mathrm{m}^{-1}/\sqrt{\mathrm{Hz}}$).

Macroscopic arrays of cold atoms trapped in optical cavities can reach the strong atom-light collective coupling regime thanks to the simultaneous interactions of the cavity mode with the atomic ensemble. In a recent work we reported a protocol that takes advantage of the strong and collective atom-light interactions in cavity QED systems for precise electric field sensing in the optical domain. We showed that it can provide between $10$-$20$~dB of metrological gain over the standard quantum limit in current cavity QED experiments operating with long-lived alkaline-earth atoms. Here, we give a more in depth discussion of the protocol using both exact analytical calculations and numerical simulations, and describe the precise conditions under which the predicted enhancement holds after thoroughly accounting for both photon loss and spontaneous emission, natural decoherence mechanisms in current experiments. The analysis presented here not only serves to benchmark the protocol and its utility in cavity QED arrays but also sets the conditions required for its applicability in other experimental platforms such as arrays of trapped ions.